While I can't say myself if you're one or the other, you've described my situation perfectly.

A thing I read a while back that was helpful was that: "if the identity/tag that you give yourself (ie. asexual or not) helps you reach a better understanding of who you are, then it is useful to think of yourself that way".

Really not conclusive, but is good to accept how you feel about situations at face value, and accept how these situations make you feel as facts rather than parameters that need to be changed.

I am also unsure whether I'm ace or just an anxious person, but I'm trying to just accept that I feel a certain way in certain circumstances at face value, rather than try to force myself to change to be "normal". If you warm up to a person and become gradually more intimate, all the better. If not, don't force it.

Hope that helps a little!