Do you think it's okay to look through my boyfriend's phone when he goes to sleep or takes a shower?
Why do you want to look through your boyfriend's phone?
I'm going to look through his text messages and see who's been calling him.
You should allow your boyfriend his privacy. Just because you are dating someone does not give you the right to control or dominate them. His phone is not your property.
Well I just want to see who he's cheating on me with.
If you are worried your boyfriend is cheating on you, then you should confront them directly and ask them face to face. There's no easy way to address that, but if they are honest, then believe them and trust in them.