boyfriend maybe texting other girls???

So lately I've been really suspicious of my boyfriend texting other girls or a girl idk. My reasons to think this is that every time he is texting near me he almost like hides his phone so I can't read the messages. He also is active on messages when he told me he was going to bed. I know that he may not be texting other girls but I just get a weird feeling. I confronted him about this many months ago and he told me that he doesn't but he's acting weird again and it's really sketchy. He also tells me I can look through his phone and that I know his password but he changed it and that makes me even more suspicious. I've never gone through his phone but I kind of want to. How do I approach this situation? Clearly there's trust issues. I know.