At the recommendation of my T, I'm currently about halfway through a fascinating and quite liberating book about Asexuality that you may be interested in.
It's called "The Invisible Orientation: An Introduction to Asexuality" By Julie Sondra Decker.
It's by far the most comprehensive guide I've come across on the subject, and has been extremely helpful to me personally. I too, have a sex drive and frequently masturbate, but I'd never actually have sex with another person. And yes, I can absolutely be Asexual.
I very highly recommend anyone with questions about Asexuality to give this book a read.