Long distance relationships can be difficult but they are not impossible. You wanted to know whether you should trust your boyfriend. That is difficult for me to answer. Only you can truly answer that question. You did not include many details about the nature of your relationship. I might have been able to give you a more specific answer if I had more details about your relationship such as: What was your relationship like before his departure? How often does he keep in contact with you? What leads you to believe that he may be cheating? If I knew the answers to those questions, and maybe others, then it may have given me insight into whether he deserves your trust.
If this is an issue that you cannot resolve on your own, then I would suggest discussing it with a therapist. A therapist can help you determine whether you are being logical and rational. He or she may be able to help you develop coping skills that could assist you in managing your emotions and fears while your partner is away. If you love him and believe that your relationship is worth keeping, then perhaps you’ll consider therapy. It could save the relationship.
Psychology Today is a popular website that may be able to assist you in finding a therapist. You may not need long-term counseling. A few sessions may be all that is necessary. Thanks for writing.