If he doesnt like you for who you are, then you shouldn't be together. You are your own person and it definitely isn't wrong to want your own time and to be left alone. If he expects you to respond in an extremely grateful way simply because he complimented you, then there is something wrong. Either he isn't mature enough to handle being in a relationship or he expects too much. A simple thank you is okay for a compliment. Or even a 'you look good too'.
If you argue about the little things, then how are you going to handle big things? I dont know how old you are, but if you go to uni or move away for work etc. how are you going to work through that? Is he going to expect you to be extremely grateful if he lets you move in?
I think you have to realise that you are your own person and a partner is meant to complement you and accept you for who you are. He shouldn't pressure you to be someone you aren't. I know it is difficult to stand up to someone you really like and say no actually, I am not confident and yes I am awkward when you compliment me. I'm not sure what he expected?
Just remember: do what's best for you. If you feel uncomfortable then get away and do what you want to do. Don't let others pressure you or make you feel bad for being yourself. I'm sure you are pretty, and I understand why it might make you feel awkward if he tries to pay you a compliment. Don't worry about whether or not your reactions are normal: if they work and make you feel better then continue.
Simply: my advice would be to do what you feel best. If he doesn't allow you to be you and introverted (there is nothing wrong with that - I am a confident introvert. I prefer being alone rather than being with my friends and I don't see anything wrong with that) then you don't need him. A relationship is about balance and acceptance. If he can't accept that you feel awkward when he compliments you, then what else wont he accept?
Be yourself and sod everyone else.