Should I try to be friends with her and see if something happens?

Hi I'm a 16 year old boy and I definitely should not be feeling this depressed but I can't help it. There is a girl I like and let's just say we have been through a few rough patches. The problem is that she says she doesn't like me but the thing is she doesn't even know me well enough to say that! She agrees to hanging out with me and stuff but she just pushes me away on that subject... Should I continue to be friends and see if something will happen or do I give up.

Whether she knows you "well enough" is her choice, not yours. My advice would be to continue your friendship but never bring the subject of who she likes up again. If she starts the conversation that will be the sign that she feels like she knows you well enough. In the meantime, if you want to hang out with another girl, do it. That may help her sort out how she feels. If she has no problem with it, your possibilities don't look very good.

I agree. It looks like she's being pretty clear she doesn't want to date. Whether she knows you well enough to judge that is her call, not yours. If you bring it up more, she may get really uncomfortable and stop hanging out with you all together.