You sound just like my boyfriend. I’m kind of a spaz when it comes to school, work, and especially sex, and if this were a few months earlier and for a few details, I'd say you were him.
Your problems with seeing each other could possibly be solved by a little better communication-- not that you have poor communication now. Try making a schedule of times you can see each other. Homework sucks so I usually feel better when I take a break to talk to my boyfriend. See if you can plan little breaks where you don't do anything but be together. No homework or work. At first those times where hard for me to work out but now its a part of my day I look forward to most. What about weekends? And try staying in to watch movies, that way you can cuddle close and not have to worry about driving to the theater. It may be less stress for her and having you physically close just to sit and relax would probably be really nice.
Have you tried talking to her and asking why she gets so panicked or doesn’t feel comfortable doing things physically? Try asking why she gets so panicked. Maybe she doesn’t know what to do? Maybe she’s had a bad experience before? Maybe she’s just not ready for that step? Talking about it is a good way to break the ice. I had a really hard time with doing anything physical with my boyfriend until he finally sat me down and asked what was going on and we had to have the conversation a lot before everything finally got worked out since I was silly and didn’t say everything all at once. So remember to be patient and understanding! If you love the girl then it will be worth it!
Just be patient all around. You’ve only been together 3 months and sometimes schedules and routines are hard to set and you’re still getting used to each other as a couple. Things will get easier and I hope this helps!