Include "person" and it sounds much better because it is more humanizing. Like "autistic person" rather than "autist" or "autistic." Works with other descriptors too.
Speak for yourself only, please. It's s fine if you prefer autistic person, but I and many autistics I know don't. The bottom line is not to teach someone what' s best but to inform them that there may be preferences and to listen to the reason there talking to, not to make blanket statements about what's the right thing.
You didn't do anything wrong, both is fine. Me and most of my autistic friends actually prefer to call ourselves autistic. Figure out what you prefer first and foremost :)
It just seemed questionable to me because it reminded me of how some people call trans people "a trans", which is kind of off-putting for me. It kind of makes it sound like "transness" is the totality of what they are rather than just being another person.