Is my boyfriend cheating?

Abby • I`m 26. NTTC
Im 24 and my boyfriend is 37.  We have been together (and living together) since August of 2013.. We have a really good relationship. We struggle with money and "live on love" from time to time. But anyways, ever since I can remember his phone is on silent 24/7.  I, on occasion, will look through it when he's sleeping to see if something's going on that shouldn't be because I don't know why else it would always have to be on silent.  A month ago I done that and noticed he had downloaded snapchat awhile back and got curious so I downloaded it as well and sent him one. Even made the name abbylovesrob. No reply. So last week I had the opportunity to snoop and I did! Found that all this time he had been chatting with a girl (he changed the name to a Guys name on there) then immediately went to his text messages.. Sure enough that same "guys" name was in his messages he had texted her.. "What are you doing sexy butt" then I proceeded to go to his Facebook and he was friends with her on there as well!!! This was the day before thanksgiving and it was bothering me so bad.. I didn't want to be in the dark on the holiday. So I confronted him that night and he admitted to it and said it was the biggest mistake of his life, he would never for the rest of his days, do anything like that to me again. Said that the reason he done it was because he knows I snoop in his phone and I don't trust him. So in my head I was thinking ok.. So if you want me to trust you.. DONT DO ANYTHING STUPID ON THERE! Am I right?! He ended up bawling and in the floor on his knees crying and begging me to give him another chance.. I agreed I would try ex swore e never met up with her. It's been a few days and my birthday is tomorrow.. I'm scared that I will never be able to trust him again. It's so unbelievable that he done that.. All our family and friends always say we were meant for each other.. That we are soul mates and I feel the same but, I can't hardly fall asleep at night now and I just want to know what to do from here & do you consider snap chat and texting cheating? I love him a lot but don't want to waste his or my time if I will never trust him again... Please help any advice is greatly appreciated!!