You did what you did because you don't trust this guy. Quite honestly, he doesn't sound trustworthy. You don't really believe his story about how "it's not how it looks." His story sounds like baloney to me. Even before this, you probably lacked trust in him. He probably gave you other reasons before this latest thing.

Get honest with yourself. You snooped because you feared this guy was playing you for a fool. That's a pretty good reason to cross a privacy boundary. If you're a person who normally respects the boundaries of others, then you need to back away from feeling all guilty about the snooping. If he has a pattern of betraying your trust, then you did what you needed to do. Ask yourself how he behaved in his previous relationships. You're looking for signs of a pattern.

Do not feel you owe this guy your unwavering trust, just because you care for him. You don't because you're still getting to know him. Until he earns your trust, you don't owe any trust to him. He may be someone who is just not trustworthy, despite other appealing qualities he may have. You then have to figure out if that's something you can put up with. It's good that you don't know how to feel now. That's you facing the reality that you do not really know this guy. Getting to know a person's character takes time. It can take a lot of time.