I think you have gone into the relationship for very wrong reasons.
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Also I do not know what to say about the interest part, her and I spoke online for months prior to me moving here. I determined that I was going to at least try to find a friend or a g/f.
So you have gone into the relationship for want of a girlfriend, not because you like this girl in particular. That's unfair to her and you need to end this before she ends it herself, as she will come to see that you have little interest in her.
You can't 'force' a relationship; sure they take work but you needn't ever have to
convince yourself that someone is right. I learnt this myself by being in a situation very similar to yours. I only realised that the reasons why I went out with the person were wrong in retrospect, however.