I think you need to examine your behaviour. I would suggest that for your husband to be that angry about being interrupted, it likely is something you do often. It is my experience that serial interrupters are almost always oblivious to the fact that they do it.
Interrupting people is unbearably rude, and can make the person who is constantly interrupted feel invisible and disrespected.
I don't think your husband handled it well by snapping at you, but I expect he was upset.
The other big issue is you crying - he was the one who was hurt by your behaviour, and by crying you were centering your own feelings, and not allowing him to have his hurt addressed (because, even if just subconsciously, you wanted him to feel bad for upsetting you).
It was then really inappropriate for you to chase him into the shower and shout at him when he was trying to remove himself from the situation, but you obviously already know that.
I do not think it's at all acceptable that your husband pushed you, especially so hard that you fell - although I expect he felt cornered when he had tried to leave. But that isn't an excuse and he shouldn't have done it.
I think you need to have a conversation which starts with you taking responsibility for your behaviour and apologising to him. That should include an undertaking to change your behaviour re the interrupting, and an explanation of how you intend to stop it happening again.
You also need to apologise to your children if they witnessed this, and tell them it won't happen again.
Your husband ought to apologise to you too for what he did. But ultimately you created and then vastly escalated this situation, and the apology for that is where this should start.