Am I in the right relationship?

My boyfriend and I have been together for 4 months. He is 21, he is extremely depressed (suicidal thoughts) and has crippling anxiety. He dropped out of uni because of his mental illness, and now isn't in the right frame of mind to get a job which has led to him having an awful relationship with his parents. He was getting money from a disability allowance but they deemed him well enough to come off it, so now he has no source of income either, so yeah, he's not well. But the thing is, I'm trying so hard to be there for him and I love him more than anything but his mood swings, inability to cope under stressful situations and raging temper which he "gets from his dad" is really taking a toll on my well-being too. I am 18 now, doing A-levels at school so I'm coping with a lot of stress right now myself, and I feel sad and responsible for his happiness too.. Every time he talks about how he feels like he wants to die, I listen really hard and try to tell him how much he's worth, but when I need to talk about something that's making me upset he always shrugs it off and somehow the conversation always reverts back to him and how he is depressed and anxious, etc. I feel as though I am giving all the support in the relationship at the moment and am getting very little in return. He keeps calling off plans to meet my parents because he is too nervous which makes me worried because my parents keep asking me when they can meet him - another added stress! I have tried talking to him about this and it worked for about a day but now he has gone back to not listening to me if I need to open up.

What should I do? Am I supposed to be in this relationship if I'm feeling so sad? Should I feel as guilty as I do for feeling upset when he's the one with depression? Am I a bad person for feeling this way?