Sometimes sexuality is not easy to categorise. At the moment, it sounds like this is the case for your sexuality.
There are words for people you want to have sex with: heterosexual, homosexual, bisexual, pansexual, asexual.
There are words for people you want to have a relationship with and do romantic things (holding hands, kissing) with: heteroromantic, homoromantic, biromantic, panromantic, aromantic.
You can be sexually attracted to people of the same sex, but romantically attracted to people of the opposite sex. I knew someone who was bisexual but homoromantic, so she fancied women and men but only wanted boyfriends. I'm asexual and aromantic, which is not as interesting, really.

Ha. I find it all the more interesting. More time to think! (I'm really not sure where I fall; Probably between asexual and bisexual but also biromantic)