Advice of ways to deal with anger stemming from guilt

I cheated on my wife last year, she found out and we have been trying to work through things but a recurring issue has been that I am getting angry at her over the smallest thing. It culminated last night when we went out for a night out, we had a lovely time but both drank a lot, which is not usual for us, we rarely drink at all these past 3-4 years.

I got really angry at her for something that was my fault and I ended up hitting her and attacking her, I don't fully remember the details, things are coming back, but my wife has told me exactly what I did this morning. I have never hit anyone before and I hate myself for it but I realise I need to address what triggered this. Yes that alcohol was a factor but I will not let that be an excuse for this out of character awful behaviour.

I am coming to realise that my anger stems from the intense feelings of guilt I still fear, and I am then taking this out on my wife. I am not angry at her, I want us to work and I want us to get through this. I don't know if that is possible, especially after my most recent actions but I need to deal with this gnawing hate for myself that I have for all my actions.

Has anyone had similar experiences, not physical violence but anger stemming from guilt at hurting someone you love that you then take out on them. We are seeing a couples councillor and I intend to bring this up with her next session but I also want to be proactive now to try and start resolving things.