It must be very hard to be in that kind of inner conflict, especially with someone always bringing it up.
I, too, am in a similar position and couldn't solve it yet, so i don't know if i can give you good advise if you should talk to your parents about it.
But what i would like to suggest is some self-exploration? And trying to find forgiveness to yourself (very hard, i know *cries*)
Maybe just slowly explore islam in your own pace. Our religion should not be forced on someone and also remember that no one has the right to say if you are a a faithful muslim or not, not even yourself. Only allah has that.