OP, I am a name changer.
DH and I have in the past lost control and ended in violence. Twice I hit him, once he shook me.
After I was violent I sought counselling and got help for my depression. After he went for me he left because he was ashamed and also never wanted to do it again and worried that with our dynamic as it was, he might.
In the end we decided that we wanted to work from rock bottom up and make our relationship work. I continued counselling and the ADs made a he difference to my confidence, tiredness, frustration and anger. He went for Anger Management which he sourced through our GP. We both went for counselling.
This is 10 years ago and neither of us sunk so low again. We still have arguments but we have better knowledge within ourselves as to how to communicate reasonably, and how to not let arguments get out of hand.
Violence is not acceptable, but I think there is a difference between living with someone who you fear (DH and I never physically lived in physical or emotional fear of each other) and having an out burst that goes much further than it should and then facing up to what you have done and addressing it.
I think that 'forgetting it' as your DH suggests is not the best option. Because you don't want it to happen again, ever, and because there are other problems in your relationship.
In your shoes I would, as separate initiatives:
Seek counselling to find your strength and assertiveness - how to make your point and stay calm and strong, and how to identify your choices in life..
Seek anger management, so that you know you will never undermine yourself like this or risk anyone else becoming the target of your anger and frustration.
Ask yourself whether you want to stay with your DH. You may have crossed the line into violence - but is he emotionally abusive? Is he always a partner who puts you down, blames you for things and refuses to act as a team ?
Then either make a decision to split - or else seek help to make your relationship fairer and more mutually supportive.
If you want to stay, and he wants to make a go of it, and if he is not EA, then you should seek couples counselling (they will not accept you if it is an abusive relationship, as in on going abuse).
Violence is serious, obviously. There are no excuses for it. But when women on MN post to say they are ashamed they have smacked their children they get constructive support, mostly, not to do it again, and re-assured that as long as it is stopped and relationship does not become toxic and terrifying for the child, no lasting harm will be done.
When we discuss violence amongst adults maybe there should be room for people to talk beyond 'go to the police'. and offer the same constructive support, in some circumstances.
Obviously if someone is living in the shadow of the threat and actuality of violence as a regular thing or a means to control they need to be urged and supported to leave. But there are cases that may not have to be black and white.
OP whatever the outcome of this, I am sorry your life is so difficult at the moment.