I just started my freshman year of college. For reasons far to specific to my school to mention, I can't attend parties or really have much of a social life.
I have plenty of opportunities to game but I haven't really been putting much energy into it.

I sat next to this girl in class, (about an 8, she would been completely out of my league in H.S.) and she starts talking to me. She asked me some obvious question about the homework assignment... I've done enough openers I know when someone does one on me ;D... I awkwardly number closed. Turns out we have like 4 classes together... we've been sorta hanging out.. texting back and forth.. sitting next to each other in class exchanging sarcastic comments etc.

I'm in strange position... I can't logistically have a girlfriend or even a girl to fool around with.. so i've almost been ignoring her in some respects.. not because i want to but because i sorta have to... but she's been approaching me when i do this. She's the type of girl that is so attractive it hurts... i hate myself for it but i like her.
I have one-itis for a girl I ignore.

I'm not really sure what to do or where I stand with this girl... I want to escalate but I'm not sure how at this point to start.

Any advice or commentary would be greatly appreciated
Thanks,
-Xerxes the Great

One-itis is a specific affliction related to placing one's happiness in the hands of a particular girl. You don't have one-itis if you are attracted to someone, all that means is... you are attracted to her.

What could your situation possibly be that you can't even fool around with a girl? Do you have handlers that follow you around? Is your dick checked for moisture when you head home at night?

What's wrong with a little late studying somewhere quiet?

hahahhah.
sorta actually...
not the dick checking but... sorta...

My phrasing was a little off, maybe not one-itis, but its just that she's the only girl. I'm really talking to at the moment and I want her to like me.

It's not easy, but possible, for me to transition to physical contact with girls i just want to eff...
With girls like her its difficult.

I suggested the studying for that reason but that didn't really work out today because its friday (the word means nothing to me personally, i have no friday nights) We just sat around in a campus dining area and talked for a few hours.
I feel like thats all i can ever do with girls... sit around, talk, and make stupid jokes.

any advice on how i could initiate the physical ? how do a turn a conversation that direction ?

Try Kino esculation. I sympathise to not having anytime. I've been very much like that in the last year with my studies and i had no time to concentrate on this. However what is your situation that you can't arrange a few hours off here and there. Your message is abit vague.