Please do not fall into the trap of thinking 'I can fix him'.
Speaking from actual personal experience, you can't. It. won't. work.
It took me a long while to understand that it doesn't matter what the issue is - MH issues, drug issues, a bad childhood - it actually doesn't matter. If they're treating you like this and you're having to tiptoe around them all the time, it is simply not ok.
This atmosphere is around you and your DC all the time - and he will pick it up I absolutely guarantee it.
I wasted FIVE YEARS of my life trying to 'help' my DP to 'get better' with his PTSD - an utter, utter, utter waste of time.
And no, he's not 'different', your situation is not 'different'. Sadly these types of people/situations are all predictably very much the same.
Sorry, I'd like to be able to say ok just do x y and z and it will get better but really, it's highly unlikely that it will and you won't ever BE able to sort anything out if you are constantly trying to manage his moods and outbursts - you can't even talk to him now because he controls the chance of any change taking place by having an outburst and that ends that avenue of the starts of a possible resolution.
When you say 'I want him to get better' it is a red flag for me OP because it's not your responsibility. He's not ill (in that way) and even if he does have anxiety, if it's causing a relationship and home life like this, then it's unacceptable for you all to suffer because of it, regardless of the cause.
It is, plainly, totally unacceptable behaviour.
I'm sorry, I know this sounds so so harsh but it's borne of personal experience and years of my life that I literally just wasted; for nothing on someone I thought I could fix. Sadly I see it going that way for you too OP.