I'm sorry but yeah, she is cheating even if they aren't having sex, she is still cheating emotionally as she is allowing a man to talk flirty to her and not stopping him while she meant to be officially with you.
I know this hurts but you do deserve better and to not be used as a doormat basically.
In a way it sounds like she wanted you to see those txts. Why would she keep them on her phone if she asked you to look at her phone?