Asexuality is as broad as any other orientation. As
@kbb0 brought up some terms that are helpful to learn, and there are tons of others. I know that there is this internal drive to find a label to help define yourself, so you know how to define to others your intent. Be aware that this can grow and change as you develope, and definition in sexuality is more a starting point than an exact location, like someone saying "I live in the Europe." It gives a rough starting point.
There are lots of questions to ask of yourself to help.
Do you have a preference in the sex or gender of your partner?
Do you prefer one on one relationship or are you open to multiple partners?
Is the emotional connection platonic, life partner, or romantic?
When it does come to physical intimacy, what does interest you (hugs, cuddles, kissing, or nonstandard sexual interaction) or are you totally hand off?
As a quick asside I had a friend who embraced her asexuality since highschool, and was very happy about it. She began studying psychology and sexuality and found that the kink community had some interest to her. Sexuality there wasn't simply organism based, but skill, interpersonal relationship, and just outside simply mashing genitalia. While I'm not recommending any sort of swan dive into the kink scene, has any of that sort of physicality interested you?