Ok fisrt off, stop hacking up your body! That right there is an indicator you need some professional help.
Secondly, if you notice there are lots of threads on this forum about LDR's and how it takes special people to be able to handle them and make them work. This is always going to be a problem becasue you two aren't close to each other as often as normal couples are and so the thought of them cheating will always be in your mind or her's. This is the exact reason LDR"s don't work for people who have trust issues.
So since you can't prove anything to her exect to keep telling her the truth you either have to deal with this until you two decided to "be" together or you will ahe to cut your losses now. And another note is she is already doing things behind your back..so your trust with her should be the issue not the other way around. And the reason she is accusing you is because she's doing it herself!
If you can't handle the thorns, don't crave the rose!!