Me and my boyfriend keep arguing what should I do?

Recently me and my boyfriend have been arguing quite a bit, whenever he comes over to stay or I stay over at his we argue at least once and it’s a bad argument. He first told me he felt I was putting no effort in, which I understand. But I have been extremely depressed recently and I don’t know if I had the capacity to be a good girlfriend to him, so I broke up with him. But the issue is i then keep going back to him because it’s not that I want to break up with him my brain just keeps telling me it’s the best thing to do and that he deserves better. I let him know after the argument that I’ve been depressed coming to my first year of university and falling out with my mum as well as just seasonal depression coming. But i don’t know if he completely understands how bad I feel.

I called him a few times because i was feeling so shit and i just wanted to talk to him and he ignored me, this made me catastrophise a lot and I decided that we needed to break up again so I broke up with him. I know this is wrong, I know I shouldn’t be toying with him like this but my anxiety gets the best of me and I feel completely out of control with what what to do with me. I know he ignored me because he needed alone time but it felt like shit and made my mind wonder too far. I again realise I do not want to lose him and i feel I want to drop out of university and go to one near home because this is what has caused my depression a lot. But I know he feels done and is tired which i understand. I don’t know how to prove to him I do care for him and want to be with him. I know I’m making him feel like he can’t trust me and it’s my fault. I don’t know what to do. I shouldn’t be completely relying on him to help me through this and I feel I’m treating him horribly

We’ve also only been dating for nearly three months, i keep feeling like we’re doomed and it’s not going to get better and it’s my fault.