You can take control of this op.
Put his stuff in a shed, send him a final text saying "your stuff is in the shed, please arrange to have it collected by Friday or I will be taking all to the charity shop." In fact if he has a friend who is local you could contact them first and say "x and I have split, he's refusing to talk to me has just left after an argument and said it's over, is there any way I could just drop his stuff at yours?" then text him to tell him where it is. That way you never have to speak to him again.
Then block his number and forget about him. I know it's brutal but it's only been seven months. This wasn't even a long-term relationship yet, regardless of how serious he said it was.
It doesn't matter whose "fault" the argument was. People row about silly things sometimes. Iirc the first row me and dp ever had was because i couldn't get a piece of software on my computer working and I was stroppy at it rather than dp but he bore the brunt of it.
the difference though is that most rows don't end up in someone needing space and then ending a relationship.
But you need to pull yourself together. I know it's upsetting but feeling paralysed and unable to breathe is a disproportionate reaction, it will take hold if you let it. Don't let it. Order a takeaway with the kids, tell them that you've split up, that way there's no chance of you taking him back, and then get on with your life.
Yes it will take a bit of time for you to stop thinking about him but it will get better I promise, and no contact will help immensely with that.