You can't build a relationship without trust. You are too young to waste time on this sort of relationship. I suggest moving on if you are not happy. There are many fish in the sea, after all.
People who are jealous tend to be the ones who are dishonest, so watch out. These types tend to believe that everyone behaves the way the do, so they are untrusting of everyone else. This may not be the case, it could be that this girl has been hurt too many times before and simply can't trust. Either way it's not a good situation and as young as you are with no binding committment to her I suggest moving on.