Relationships are built on trust... if you feel your relationship is not is not progressing in the trust department... then you might as well get out now. It doesn't matter if a person cheats on you or not (well it does, but that's not what disrupts the relationship)... what matters is can you trust them? If you feel that you cannot... then you either need to find a way in which you can trust them, or you need to call it quits and find someone else.
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen