Is sharp a noun or not?

It depends on how you use it. If you are talking about something that is sharp, like a knife or a note, then it is an adjective.

If you are talking about a sharp, a type of note or needle, then it is a noun.

A good way to tell the difference is whether you can substitute another adjective, like a color, and have it make sense.

A knife can be red, blue, dull, or sharp. WIth the sentence "This is a sharp knife" you can substitute a lot of adjectives and have it still make sense.

However, if you are in music class and telling someone "This is a sharp, and this is a flat," it isn't going to make sense if you say "this is a blue," or "this is a green," or "this is a dull." If you can't substitute another adjective, then it likely isn't one. :)