Whenever you have reason for suspicion in your relationship, you have two options. You can either ask your partner outright about your suspicions, or you can look into it yourself. You chose to look into it. It is ok to feel guilty about it, especially since it is something you would not normally do. That is your internal "police", your conscience, telling you that you did something you feel is wrong. It is a good sign that you have good control over your own behavior and follow societies rules.
You are not a terrible person for snooping. It is human nature, especially in a relationship where you feel strongly motivated to protect yourself. Your boyfriend is giving you signs that something is wrong. It provoked you to feel worried and you reacted. Yes, it was not the best thing to do. But it happens a lot in relationships, more often than you may know.
The best way to get rid of your guilt would be to admit wrong. For you, that may mean apologizing to your boyfriend. But don't allow him to make you feel worse about it. Once you apologize, it is up to him to forgive you. If he does not, then that becomes an issue about him and not you. You will have done what you can to repair the problem. That is all you can do. Anything further is about his inability to let go and probably about his guilt for what he is doing to you, which is cheating.
PS I got your request for this additional question this morning. I'm sorry I could not catch it in time. Just Answer requests to a specific Expert only last 10 minutes before they are put into the general queue. Since your question did not have my name on it, the Expert who answered did not know it was for anyone specific. If you would like to work with me again, just put my name at the beginning of your question such as "Kate, I wanted to ask....." so if I'm not on line and can't catch it, the other Experts know it is for me and will leave it until I can get to it. Thanks!