Is this cheating?

Yesterday me and my bf had a small and stupid argument, nothing out of the ordinary nothing important but something in me told me to check his phone.

Iv never once in the 5 years we’ve been together felt the need to check his phone, Iv never ever not trusted him.

Cut to me checking his phone, low and behold there’s messages on there from an unknown number. Nothing flirty but you can just tell there’s more to it.

He went out with his friends Saturday night and these messages start then.

Basically her telling him where she is then a couple messages of him asking her to come meet them in the bar they were in.

She stopped replying but he carried on the next morning when he was in bed with me. Only ‘good morning’ and ‘how was *** bar last night’ she never replied.

I didn’t know who sent the messages at the time but I had an idea it was a girl. I took a photo of the texts on my phone then went back downstairs and asked him if there was any reason why he was arguing with me over something so small is there anything he wasn’t to tell me. He said no.

I couldn’t let it go I just knew something was up so I searched the number and straight away it brought up a girls fb page. I was raging so I asked him who it was and he stood there and lied to my face. Saying he doesn’t know who I’m talking about, there aren’t any messages on his phone (he handed me his phone and he’d deleted them) then I showed him the messages I’d took a photo of. I can’t remember what was said then because I ran off in tears.

He said he was drunk, which is a fucking shitty excuse, and he doesn’t remember who she is and that nothing happened more than texts. I believe that nothing more happened, but because she doesn’t seem interested at all on the texts not because he didn’t want it to.

We have a 2 year old, and we’ve been ttc a 2nd for nearly a year. The texts are harmless but it’s the intention behind them that really hurts, and the fact he still tried to talk to her the next day. What would you do? Will I look stupid for staying? Or do I need to break up my family over these stupid texts?

Help please guys I’m distraught 😭😭