Ladies am i tripping out please respond. I think he might be cheating on me

So me and my boyfriend have been together for 7 years . 2 kids 4 years old and a 6 week old.

Well he always works early 3-4am and i would have not found this suspicious if he would not have done this but...

I was asleep but not fully asleep in bed with him and I’ve seen he got a text message and kept looking as if he wanted to reply but didn’t . So i was facing my back on him and as soon as i turn around to face him he looked like he was about to click on the text and as soon as i turned around he immediately turned off his phone (that is what made me so suspicious because when a coworker texts him he will text back no problem when i am next to him) but as soon i turned he shut off his phone so quick . So i waited . Once he got up he sat down opened his phone and replied i saw those fingers texting away so clearly.

I did not want to say a word but i just had too i simply asked “who texted you?” And he said “NOBODY” and i said “mmm are u sure because i clearly saw u got a text message when u were next to me and it seemed as if u we’re going to reply and u put ur phone down so quickly” and he responds and says “umm no ur seeing things u need some sleep” and i said no i don’t i saw u text back like don’t lie then he proceeded to call me crazy and i shouldn’t start fights . Like is it just me ? Or if this happened to u ladies would u be just as suspicious?? I have also known him for 7 years and i know when he’s lying to me

His response to me really pissed me off as i am not stupid i saw the text clear as day

I also have trust issues as he was cheating on me online on Snapchat flirting with a girl. And when i confronted him with this time around his tone of voice was EXACTLY THE SAME his body language was the same as the first time around. I forgave him as it was no physical cheating when he first did it.

I also told him that if he was lying that I’d eventually find out but i mean that literally. I know his password to his phone and he doesn’t know that i know it. I actually saw his password one morning when he thought i was sleeping . I used the password recently to open his phone but did not check it . That’s another thing is that he does not let me see his phone or ever use it he has a password and will never tell me his password ever.

Should i look through his phone ? Not sure if that’s okay or not but i just know one thing is that if he is cheating i will not give him another chance and will be kicking him out immediately.