Aromantic and asexual are part of the same spectrum, and many people are both, but they're not mutually exclusive. Aromantic means you are not romantically attracted to anyone, while asexual means you are not sexually attracted to anyone. You could be sexually attracted to people but experience/desire no romantic feelings for them, or you can also be romantically attracted to them but experience/desire no sexual feelings for them.
However, those are orientations, they're what you are naturally. When you say you don't "want" to date people because of a certain issue, that comes off more as a conscious decision not to engage in romantic and/or sexual relationships rather than experiencing an innate lack of interest. That sounds more like abstinence or celibacy.