Cheated??

My boyfriends texts are purple, the other one is his girl co worker… he says the only time he hung out with her was 3 times but with 2 other co workers. Said they all smoke together on their breaks. He works 10pm-7am.. he uses my car to go to work and all of a sudden he’s worried about keeping it constantly clean.. sometimes my kids car seats are undone when he comes home the next morning.

He also would always come home on his hour breaks and his job is only 5 minutes away.

He swears all this was a rumor and that nothing has happened between them.

But why on earth would she say “I’m not doing anything with you anymore because you have a gf” I feel like that most definitely means they did something together especially since she says “because you have a gf”

He says I’m overreacting and swears he never did anything with her only smoked with other co workers around.. I don’t know what to do without more proof. I tried messaging the girl but she won’t reply. I think he’s probably asked her not too.