My husband might be cheating on me????

Okay SOOOO. I’m 29 years old, my husband is 33. We have been married 2.5 years and have a 16 month old baby girl who is so perfect. I am now 5.5 months pregnant with twins. Lately, however, I have been catching my husband in lie after lie. He works in the restaurant industry - very late nights getting off around 2-3am and then has been going out drinking and lying to me about it. Well on Thursday night he didn’t come home till 5am and was drunk. He lied to me about where he was over the course of 3 days and like 5 hour long conversations making up really intricate lies. So to find out the truth I went through his computer and found he was at the bar but couldn’t figure out with who. I saw some texts between him and a female coworker where he was calling her “boo” and planned to confront him about it when he got home. When I asked to see his phone the texts from her were deleted. Now I think he’s cheating on me even though I would’ve never pegged him for a cheater before. He swears he’s not and says he was at the bar with a guy from work but I don’t believe him. I don’t know how to gain trust back and today is his first day back at work since and I’m losing my mind thinking he’s with another woman.

I need advice on how to find out the truth and how to stop my mind from the circles it’s running in.

EDIT: I have checked phone records but they don’t include iMessages and both my husband and the woman have iPhones 😞