Hello BroccoliOfLife,
Yes, you can absolutely be asexual and have crushes/want a romantic relationship! Most non-asexual people experience romantic and sexual attraction at the same time and don't differentiate, but romantic and sexual attraction don't have to go together. For every sexual orientation, there is a corresponding romantic orientation (heterosexual and heteroromantic, for example), and your romantic and sexual orientations don't have to match up. To me, it sounds like you could be heteroromantic asexual because you describe being romantically but not sexually attracted to men, but your attraction to women seems to be more platonic.