Message from woman in boyfriends phone

I posted this last night but can’t find the post anymore to see any of the replies.. IM SORRY

So I went through his notifications b/c I don’t have his pw. He left his phone in the car for about 30 mins. Didn’t see too much of course, but I saw a message from a lady saying “how has your day been” so they must of had an ongoing convo going..I’ve never seen her msg before on his notifications. I suspected he has been talking to someone else, he kept trying to assure me he was not. But, BEEN THERE DONE THAT with prev men and their always lying. I told him I’m never wrong when I have a feeling and he said this time I am wrong and that he would not lie to me. I’ve never caught him in a lie before. Even though from the jump due to my bad trust issues I never trusted him..And what makes it harder is he’s older than me so sometimes I feel he wants someone closer to his age. These past few weeks have been rocky. We usually see each other on Saturdays and we didn’t the last two because of arguing and that made my suspicion raise even more. Now we did delete tinder together (that’s how we found each other) and although before we got together I saw notifications on his phone I haven’t seen them anymore. He ft me he deleted tinder and shared his screen so I could see that he deleted it.

Part of me is like he would not do that. We haven’t been together long though… but the other part of me is it’s happened to me several times in prev relationships plus me and him been arguing lately.. would you feel a certain way about the message????