I'm pretty sure my friends boyfriend's cheating on her...?

I have second period with her boyfriend, and sometimes this girl waits for him and they walk to their next class. But I thought nothing of it cause their friends and they eat lunch together with the rest of their friends. And my friend and I sit in a totally different place. He only sometimes eats with us sometimes. But when he started walking with her to class this next time they were kinda shoving each other and flirting. And I was kinda worried, but I wasn't gonna say anything because it could have just been friendly and I was interpreting it wrong. But today my friend went home sick, and I was walking from third period, and I passed him in the hall, moving behind that other girl, with his hands on her hips from behind, shoving her along with him. We made eye contact and he quickly looked away. And I know him, he knows me, and he knows I'm his girlfriends best friend. But I mean, this couldn't be friendly the way he was touching her. He touches my friend the same way. So I'm not sure what to do. I don't think it's my place, and I don't know anything for sure, and I don't want to cause problems. But later that day I asked how my friend was feeling and she said better cause her boyfriend was telling her how much he loves her. I got the feeling that he only did that cause of what I saw in the hall...

My questions are,

Do you think he said that for that reason?

And what do you think I should do?

Thank you for all answers. I appreciate it.