Slept with someone while broken up

My and my girlfriend broke up earlier this year and while we were apart, I contacted her multiple times asking if we could ever have a shot again or get together again, and all her answers were no. I didn’t know what to do and months later I decided to sleep with someone one time to forget about everything. I was so hurt and I thought that it would make me forget things. This was completely out of character for me and I regretted it right after. I just didn’t know what to do with myself. A while after that, my girlfriend asked to get back together, and I didn’t want to lie to her so I told her that I was with slept with someone and now she won’t look my way. I get that it’s my fault and I take accountability for it. I’ve never cheated on her or done anything remotely close. Im so upset and angry at myself I don’t know