Ten Minutes: Part 1

I love the idea of using the alternate perspectives in your writing. This is really original and works really well. There is a LOT of dialogue in this work though, it might be better with a little more description. I appreciate the fact that this is a people piece, but it would be more appropriate form for a script or something, I think.
Still good writing, just needs a bit of editing.

Okay, so. The characters are rather interesting, and the inner dialogue of thoughts is interesting and helps bring them to life. Outside of that, I feel like you could use more imagery in this piece. There's a few points where you go at that, but it could use buffing up and additional imagery. Plus, some of the added things from imagery may help it flow a tad bit better. Oh, and everything I say are just suggestions. If you really don't agree with things, or you see something I didn't point out that you want to change, do what you want. It's your work, and you shouldn't bend it to the wills of others.
And I'll give you a more specific breakdown:

"I was in the middle of lighting my cigarette when Joci just had to bring it up." <- So, you start the piece with this. It's a good hook, and the next line of what "it" is helps in the hooking as well. However, you never mention the setting. When Madison mentions going to history, the reader can assume that they are at school, but that's only a guess. Adding in some setting would help greatly.

"I paused briefly, the flames from the lighter warm in my hands." <- I actually quite like this line, so I'm just going to point it out to you for giggles.

"Joci stared at me as I tucked my red Bic back into my jean pocket, and I took a long drag." <- Here, I feel like the sentence structure makes what you are saying choppy and disjointed. I'd suggest changing it to something like: "...I tucked my red Bic back into my jean pocket and took a long drag from the cigarette." And I would recommend adding a bit more detail in that. For example, "my back jean pocket".

"I stared right back at her." -> I feel like this line is a bit off of the character. Up to this point, Madison is trying to keep up a cool, calm facade, and she seemed a bit distracted by her lighter and cigarette. Maybe say something along the lines of "I met her gaze." Or something that implies (or, better implies, because I feel like this is what you were going for, even though it was lost in execution) that she's giving her full attention to Joci.

"I froze with the cigarette in my mouth." <-Yet again, a bit of description would help a lot. Like how was the cigarette in her mouth? Was it dangling? Hanging? Just chilling there?

"I exhaled smoke." <- Here as well. How'd she exhale the smoke? Maybe throw in something about the smoke or its taste or smell.

"I clenched my teeth together." <- The together is a bit redundant at this point. Clenching one's teeth implies they come together. And this is where you hit the balance of adding things in but not adding too much. There's a fine line between helpful descriptive words and just excess junk. One of my teachers once told me to think of it like each word costs $5, and you're a poor writer. So, every little word you buy better be completely worth those $5 of your nonexistent money.

"I tossed my cigarette to the ground, and stomped it out with my Converse. " <- The second clause is dependent, so the comma isn't necessary.

"I mumbled, shoving my hands in my jacket pockets." <-Here, more description could be used. You could say something a bit more descriptive about the jacket. Say, is it a hoodie or a letterman or what?

"I just walked past her, making my way to class." <-Again with "walked" here. Madison's being sulky and has her hands shoved in her pockets, so just walking seems strange. Maybe she trudged along or she dragged her feet as she walked?

Comment about POV changes: I'd highly recommend breaking the story up into different points based upon the POV changes, so there is only one POV per part or chapter or whatever.

"Mom parked in front of the high school, and I looked towards the doors." ->Yet again, a few words about the doors (ie something like "the glass doors" or "the double doors") and the school (ie something like it looked like a rundown old prison).

Another nonquote comment: You don't have to have so many short lines. There are various things that could be combined into paragraphs, which will help the story flow better.
"The dog ate the food.
He liked the food."
Reads differently than "The dog ate the food. He liked the food."

"“Are you sure you don't need me to come in with you?”" <-It wouldn't hurt to add in what his mother was doing here. Like maybe looking worriedly at him.

"I didn't need her trailing after me everywhere also." <-I feel like also is weirdly used. Something about it just bothers me. Maybe it is just me, but I think something like "as well" would flow better.

"I opened the passenger door, and stepped out onto the pavement. " <-Yet again, the second clause is dependent, so the comma isn't needed.

"I shut the door, and turned to wave at her as she drove away. I watched as she signaled left, then took off towards our old/new house. It was the one we sold when we left two years ago, and it was still there. Exactly the same." -> First, another extra comma between an independent clause followed by a dependent clause. Next thing about this section is the same sentence structure: "I shut. I watched. It was. It was." Change it up some. Don't do subject, verb, other stuff. Change up the sentence beginnings.

"I started walking towards the front doors, hands in my pockets." <-How were his hands in his pockets?

"Before I reached the front doors, I stopped and just stood there." <- I feel like the "before I reached the front doors" is a bit... open. Where was he in regards to the doors? Right before them? Halfway between where he got out of the car and where the doors were?

"I looked up at the wood sign with a large “Welcome!” carved in black. I remembered looking up at that same sign when I started as a freshman here in grade eight." ->Okay. I feel like you could give more description to this sign. Where did it hang? Was it faded? Was the wood or paint chipped? Was there any graffiti or such things? Also, you use sign twice in two adjacent sentences. You can use something like "the same sight" for the second one, or you could say something like "that same old sign" and maybe then elaborate on how the sign looked worse now? Maybe you could add the description of the sign as it is now after you mention it being worse off. Just play with it some.

"Memories surfaced, and I recounted endless basketball games and practices, several parties, and countless looks and waves from girls. " <-Description needed alert! What were the parties like? The girls? Looks? Waves? Practices? Games? Did the memories surface in a swirl, or did they come in flashes, or what? Lots of potentially good stuff could be added here.

So, yeah. My lovely, long critique. Essentially, I feel like you just need to work on your descriptions of things. Find the perfect place between too little and too much. It's hard to get there, and it takes lots of work, but it'll come with practice. And a few well placed descriptions can help beef up and slow down your story. Right now, I feel like everything is sort of rushed, and the extra descriptions would help immensely. Outside of that, though, this is pretty good. It could use work, but professional writers will spend long amounts of time on one thing. Sometimes poets take years working on just one poem. It takes patience and time, but the words will eventually reveal themselves and fall into place. And quick piece of advice for writing: don't force things. If the words just don't want to work, then try something else.

That was a mess. Really, a total mess.
You need to pick one Point of View and stick with it, or make it abundantly clear that there are TWO PoVs written in first person. I got halfway through it before I realized that was the case. It blended both people into one. And then that third person interjection telling the backstory didn't help with the jumpiness of the narrative.
Also, this thing's way too long. Break it into thirds, or fourths. At the very least, cut it in half. I felt like I was drowning beneath so many words (compounded with the jumpy, non-sensical narrative). So please fix this.
Hope this helps!
PS- Minor technique things, such as "to try and go" [or some other phrase] should be "to try to go", and then some other smaller things I forgot that you need to check back and fix.