Not fully trusting someone is not odd at all. Especially if you are close to someone. You want to be fully open and honest, so any worries/fears you might have are natural, as you're making yourself vunerable to them.
That aside, I can tell you my gut feeling has always been right. There are some people who are paranoid and aren't often right. It is hard to tell whether you might simply be trusting her for 'a reason' or you might not have a 'good reason' for that.
I never had a reason to distrust my previous partner. Or so I thought (but I felt differently about it, I felt he wasn't being open to me about a few important things). He never would talk openly about any issues he might have, letting stuff build up and get to him. Mentioning on multiple occassions he should talk to me, he would say "nothing's wrong". I started to more-and-more distrust him when he would say that. Sure enough, I could start to predict when he would get upset, as I could see when he wasn't open to me.
We wouldn't have even had a relationship if he was honest with me from the beginning. So 3,5 years together with someone who never wanted to be with me in the first place, as it turned out.
Anyways, you can always get a feeling to not trust someone, but you don't have any 'logical' reason to distrust them. The mind picks up body language you might not be consciously aware of. It is possible they might not be honest to you, but to what degree would be hard to tell.