I've only been going out with my boyfriend for three months, but I want to break up?

[Josephine]

I'm a sophomore premed in college and my boyfriend is a physics major. I like him a lot, and he tells me he likes me too. However, I'm on my winter break and haven't beagle to hang out or spend time with him (my parents don't like him, and don't like me hanging out with him). We weren't even able to hang out on New Year's Eve! I'm starting to think that we should break up, even though I like him so much. I just feel that there's no point in a "long distance" (his college is half an hour from mine, and he lives 30 min away, too) relationship if we aren't able to talk.

My parents are overprotective and took away my phone, so him and I have been communicating via Facebook for the past two months. I noticed that he reads my messages (Facebook notification) but he takes hours or days to respond. What's happening to us? He invited me to his New Years party a few days ago, but I couldn't go because of my parents.

Should I break up with him, or should I keep going with it, since I like him a lot and want to keep the relationship (my breaking up with him would be mainly to allow him to be "free" and date someone who is better suitable)? Thanks, guys.
When school starts, him and I don't have time to hang out because we'll be busy studying.