Trouble with the BF

Kaley
So, long story short. I've recently been offered a traveling position with one of my jobs. This offer gives me a chance to travel to states I've never been, and only be gone 10days once or twice a month. My problem is, my boyfriend. We've been dating for almost a year now, and we recently moved in together. When we first started dating, I ended up catching him on Tinder, looking up other girls on Facebook, but never talking to them as far as I've known. When I caught him he lied to me about it, until I told him I've seen it with my own eyes, then the truth started to spill. Anyways, I've had a hard time trusting him since then. I'm worried if I take this position, that the same thing is going to happen since I won't be around every day. What should I do? Am I crazy?