If you mean that this is the only girl you are interested in, then just saying that this is my girlfriend is enough in Canada, and I am pretty certain also in the US. If you want to make it more clear to your parents that she is very important, then besides saying "girlfriend" you could say that "she's the only one for me"
Solitary is not something that you would use when discribing a relationship.
I am not a teacher.
Student or Learner