Is AUTHOR wrong in the post ? POST : Throwaway, cause his sister uses reddit.

My boyfriend has very recently started to develop symptoms that we can only describe as depression. His mood is low, he doesn’t laugh at anything, he isn’t affectionate, he looks exhausted, and he just wants to sit and play on his PS4. I’m trying my best to be supportive, encouraging him to book an appointment with the doctor (I don’t have permission to for him), and he agrees but he never does.
He used to get severe headaches everyday so I was used to him lying down for 3-4 hours leaving me alone with our son, but now he never helps. If I ask for something, there’s only a 20% chance he will get up from his game and do it, and he is always mildly annoyed with me that he had to.
I am exhausted, and burnt out. He works 6-7 hours a day 5 days a week, and stays up until 3/4am playing games but I am constantly looking after our 9 month old. I snapped at him a couple of days ago after he complained I didn’t wash his shirt with “Can you give me a fucking minute?” and he has been cold since. I tried talking to him a couple times and apologizing for losing my patience but he won’t have it. He just replies with things like “Just tell me you don’t love me anymore” and “I learned my lesson, I’ll just shut the fuck up”.  

Today, he told me he was going to gamble half of his paycheque because he worked hard for it. I didn’t want to pick a fight but I told him I thought it was a bad idea. We had a huge argument after he told me to go live with my parents if I didn’t like the way he lived, and I listed everything I do around the house for our son since he is not contributing, and that I don’t expect a 500$ blowout reward for it. He told me I knew how he was feeling depressed, and that what I just said was abusive. He finished by accusing me of cheating on him, brought up every mistake I’ve ever made, then blocked me and hasn’t responded in hours. 

I just want to know if I was the asshole. I was fuming when I sent the message but looking now, I’ve never been in a relationship with someone who is depressed before and I feel like what I did was irreversible and cruel. He doesn’t mean to do what he does.