Hello & Welcome to Just Answers.
You're in a tough situation, but I do think that counseling will help you - either individually or as a couple. It sounds to me like you've got a group of questions/issues that could be sorted out pretty quickly, and then you could decide on a plan of action.
Signs of cheating? The web is full of pages that will tell you anything from looking at another woman is cheating, to cheating but admitting it isn't cheating. In the end, the only thing that counts is if you feel secure in your marriage. If you don't feel secure with his level of commitment, it could be in your own head, or it could be your gut picking up clues that should be discussed. No matter what else happens, if you think he's cheating, your marriage isn't going to move forward, and that is a very important issue.
1- Ask to see his phone and get that out of the way.
2- Ask him to help you face your insecurities, and commit to working with him on that problem. He can't make you feel safe without your participation. If that involves counseling, then you take the first step and set it up.
3-If none of that works, then get counseling for yourself so that you can either find the parts of the problem that you can change, or get support for being in a relationship that you don't feel safe & secure in.
You're young and in a new marriage...it's normal for your fears to surface and it's also normal to need help to work out the bumps in the road. Get help now before you have bigger problems that are harder to solve - you'll feel much better.
Take good care of yourself.