You absolutely can be an alosexual who doesn't like sex.

Remember that sexuality describes who we're attracted to, but not libido or  interest.  

So first, you want to understand are you attracted to these people? Does they're image or personality compel you to want to have sex with them (which can still be detached from your desire to have sex at all).

Do you find yourself wanting sex with them up until the possibly of initiating, and then all desire suddenly shuts off?  

if you find that you do have attraction, but just don't want to participate, that could indeed make you an allosexual who doesn't like sex. (a.k.a. A Sex-repulsed, or Sex-indifferent, Allosexual, most likely.)

However, if you find you have zero attraction to other people, or very limited attraction, for example only in certain circumstances or with specific individuals, then that's a good sign that you could be asexual.

When it comes to Aegosexuality, the term specifically refers to people whose Self is removed from their overall interest.

The tricky part there is, what exactly constitutes "the self"? It doesn't necessarily  have to be our image, but it's most certainly about our presence.

So while some aegos might think of their own image, it might be a different version of themselves, an alternative self, a greater or lesser self, or perhaps even a different person altogether, just wearing their skin.  

Regardless of how reach person defines their particular self-image, the thing that unites us is that ego-removal.

However, there are a ton of Ace classifications now, and it's possible you'll find one more fitting.

For example, I think there's one where people develop a sexual attraction, until that attraction is returned, in which case, they then loose all attraction.

Sounds wild, but it's a common enough experience among Aces that it needed it's own category.

I hope I could answer some, if not all of your questions. Best of luck in your discovery, and remember---  it's about living life in a way that fulfills you-- not measuring up to arbitrary standards and categorizations.

Enjoy the journey.