So I like girls and I would only engage in a relationship with romantic feelings, and I have no sexual feelings or sexual urges towards anybody. So what would I classify myself as?
Well, there are tons of labels. You could be: Homoromantic. Asexual. Gray-a. Demisexual. Those are similar to fit what you described. Or you could stick with lesbian and just tell your future or current partner you are not comfortable with sexual intimacy.
You're still a lesbian but lack sexual attraction, which would classify you as a homoromantic asexual (or grey-a asexual, demisexual).