The thing is that the last contact I had with my HR contact was 2 months ago and I don't start work for another 4 months. Is it appropriate to contact my HR contact just to keep in touch?
It is definitely appropriate. I suggest having a clear purpose behind the communication though, so something along the lines of:
- "Hi, I wanted to let you know I am still on pace to complete my degree by MM, YYYY - is there anything I need to do in the meantime?"
- "Hi, I am going to be starting full-time after this semester and am wondering if I have any paperwork or other documentation you need from me (transcripts, etc) at this point"
- "Hi, I am an intern-fulltime hire starting in May and have not heard anything for two months - I just want to confirm I have no current actions required of me"
- "Hi, I just want to confirm the only action required on my part for the next few months is to send my transcript"
Don't just go "hi, I'm freaking out that you haven't been constantly emailing me" because in all honesty it's likely your full-time job got put onto the "deal with closer to spring" pile and probably won't be seriously processed until much closer to the time you are to start.
Or am I worrying over nothing?
Honestly, it's not a big deal to email the HR people. Larger company HR people will probably receive, process, and respond to most of your emails very quickly and unless you bombard them even asking once every few months will probably be unnoticed. This is in a very real sense what they do on a daily basis.
I also would not worry about not having heard anything from them unless you had good reason to suspect the company is having financial difficulties. This exact situation actually happened to me - I had a job starting after spring and emailed the company in about exactly this point (having not heard anything for two months, I emailed them on 1/7..) and they had been in the process of canceling offers, etc. But at the same time, this has also been my exact experience with many other delayed offers due to schoolwork which did not have any problems.
Don't take it to mean something unless you have a good reason to suspect something.
If I were you, I would send a quick, professional email to your HR contact (feel free to use one of the above or something of your own) just to reassure yourself though. As someone who has also gone through the process even a 10 second "Nope, we'll get back to you closer to May!" email back from HR can make you feel a whole lot better about the process.