School magazines would not really count. There is far less competition, so it doesn't necessarily mean you are anything special.
And all you really need to do to check out small publishers is get a copy of the writer's market or some similar publication and see what the guidelines are for submissions. Those also tend to have magazines and journals. Or you can always do the ever popular google search. I managed to get into a magazine that pays because of one of those.
As well, check out the covers of books you're reading. They might have websites for the publishers. If they do, check out the websites and see if they have any guidelines.
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