Could he be cheating?

So tonight after my husband gets home from work he is acting pretty tipsy. I didn't get why and I kept asking him if he had been drinking and he just denied it over and over. So I checked our bank account and it says he went to the bar and got a couple beers. I get why he would lie to me about it... I grew up with an abusive alcoholic dad and it's a struggle for me to go let him drink with friends. It's still not okay to lie to your wife. Anyways after talking about that, I had forgiven him. Then later after he fell asleep I went on his phone history. I know, it seems like I'm a crazy wife... But I just didn't feel right about the whole thing. So I go on there and find that he was on a site called Meetme. I know exactly what that is since that's where him and I actually met. I wake him up and ask him why it's on there and he says it was a pop up ad... That sounds like bs to me. Now he won't let me see his phone again because he says that I always make a fight out of nothing. I want to believe him because I'm 32 weeks pregnant. He's never done anything like this before so it's not like he has a history of cheating or anything. Am I really making it a big deal when it's not or should I be worried?