I punched my girlfriend and made her cry, what can I do to overcome this problem?

Anonymous
We have been living together because we're gonna get married next year and we got into a huge argument today because she was out with her friends and I saw a picture of her with a guy, she said it was her friend, I got angry and jealous and we got into a huge argument and I started yelling at her and I could tell she was about to cry because her voice cracked and her eyes were getting watery and we kept fussing and I lost my temper and punched her in the nose and she ran into the bedroom crying. I ran after her when I realized what I had done and her nose was bleeding and she went into me and was crying and she said she didn't want to leave me and still wanted to be with me but she wants me to go to anger management classes but I will not. I love her and she's so sweet and I hated that I did it to her and I said I was sorry and she said she forgave me and we hugged for the longest time but as we were hugging she flinched. Sometimes I want to just punched her again and slap her. I check her messages without her knowing too. I don't want her to be afraid of me or nervous around me, how can me and her both overcome this issue together?
I punched my girlfriend and made her cry, what can I do to overcome this problem?
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