My first thought would be whether you don't experience sexual attraction to real people or whether there are other reasons why you turn people down... some kind of emotional aversion. From what you've said though, you have things in common with other people who identify as asexual. Other asexuals have described having fantasies about people who don't exist while not experiencing attraction to people who do, or about being aversive to partners because of a fear it will lead into unwanted territory.

You don't sound anything unusual to me, but if your apparent lack of in-real-life sexuality bothers you, then you might want to seek therapy to either see if you can correct what you see as a problem or else to help you come to terms with how you are.

If you feel now that you are asexual, there is nothing to stop you from using the label. If you later feel that you aren't asexual, no one is going to tell you off for using it. As for "a strange desire for the unreal"... I don't know, maybe you could call it a type of fetish?

Don't feel weird and ashamed You are just as human as anyone else.