My boyfriend is always on his phone

Megs
Whenever I'm with my boyfriend, he's always on his phone. Soon as he gets a notification he has to check it and respond. But then if he's with friends or anytime I'm not with him and I message him, it'll take hours and hours for him to respond. Sometimes he won't even respond. It just confused me how hes always on it when I'm with him. I feel like it's rude and I told him it bothers me, but he continues to keep doing it. 
Also, he picks up my phone and checks it and does whatever he wants on it. But if I even touch his phone at all he freaks out. I've never even been on his phone. He won't even let me look through pictures we took. It's not that I want to search through his phone, but his behavior is strange. 
Any suggestions?