Am I overreacting on this trust issue

About a month ago me (M26) and girlfriend (F25) got into a real bad argument about her not being home when I would get out of work. It was getting to the point where she would spend more time with her family then with me. We ended up taking a break she said she just needed space so she stayed at her family’s house . 2 weeks into our break I came to realize how I was not the perfect guy I would not show her love or affection because I was very busy with work doing a lot of overtime trying to make ends meet. I was able to convince her to come back home to sit and talk all though she was very hesitant because she described she fell out of love from me , saying I was not going to change , she no longer wanted to be in a relationship and even telling me to consider seeing someone else. I was able to plead my guilt and show her that I was indeed going to play my part in our relationship , I kept asking her if there was another man because of the way she was acting distant , she ended up admitting there was a guy she was talking to and said it was nothing only text she even showed me what I thought was the entire convo they had which was a boring not romantic conversation of them saying good morning and talking about their day. She began to cry and ask for forgiveness when she seen the pain in my face. I ended up taking her back. However 1 week later I was able to find out that they did indeed hung out 2 days before I plead my case to her by pretending to be her in messenger (I know not the right thing to do) but I had to know the truth , the guy admitted he was not confident and shy so leads me to believe they didn’t do much but he was very explicit showing what he really wanted from her . She began to cry again and said it was nothing but a mistake . We’re currently trying to fix it but I don’t feel like the trust is there anymore . Especially it only being 2 weeks apart from each other for her to act like this .

TL;DR don’t know if this is considered cheating , I’ve never thought anything like this would ever happen in our relationship especially having a family for about 10 years now with 2 kids .