Just take it one step at a time, and for the most part, 'live in the moment.'
As for your worries about her possibly cheating... well if she were cheating right this second, there's nothing you can do... and if she remains 100% faithful, there's no way you could know that either. You have to give her the benefit of the doubt and assume she's faithful to you until proven otherwise. Trust is an important part of a relationship... practically a foundation in which the rest of the relationship is built from. So you have to trust her when there is no evidence of wrongdoing.
In a situation like this... patience is the key. You will have to keep the lines of communication open and visit her as often as can be arranged. If you feel you cannot do this... then I would suggest breaking it off with her.
Long distance relationships are very difficult because of the loneliness, uncertainty, and temptation. So the choice is yours... either stick it out with her or break it off in favor of looking for a relationship with someone closer. There is no right or wrong choice here.
"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