The only thing that I noticed here was that a few times to add some unnecessary phrases onto the ends of your actions...
As I came to, a light shined in my eyes
As I came to...?
Rolling my eyes, I stood up and walked over to him with my hand outstretched for a handshake. He grabbed my hand and used it to pull himself up instead of shaking it like a normal person would upon meeting someone.
I don't think you really need the part about how a normal person would shake hands - it is inferred.
"Alex," I introduced myself. Alex was short for Alexandra, but who would want a name like that, let alone introduce herself as Alexandra every time she met someone?
the part about Alex explaining why she doesn't introduce herself as Alexandra seems a bit run-on-ish. It's not a run-on, but I think you could make it more succinct.
"Must you know everything?" he asked. I nodded because I still wanted an explanation for his actions.
I don't think you need the 'because' part here. Her nodding tells the reader she does want an explanation.
Hadn't you been having dreams of falling?" he asked knowingly.
This is probably just me, but I have a great hatred for the adverb knowingly.
"Run!" he half whispered, half ordered.
I don't know. I just really don't like the haf-this, half-that thing. I think if you could find another single verb that encapsulates the way he is saying this, it would bring this chapter to a sound conclusion.
What I really loved about this piece was your beautiful description; you varied your sentence structure well and had some great word choice. Your first person style is humorous and endearing - I love it. It just read so naturally. Really great job on this chapter, Roy.
