Verified answer

かわ is indeed short for かわいい, but you would not use it by itself as far as I know (*I say this because I am not a youngster anymore and might be little outdated. lol).

I know a word that use かわ as cute which is ぶさかわ. It is ぶさいく (ugly) + かわいい (cute) which indicates an object (person, animal, character, etc) is not really cute or bit ugly but has a part or an impression that makes them cute overall.

Additional note:

I asked my cousin and she confirmed that かわ is not used by itself.

You would not say "あの子かわ!" but "あの子かわいい!" to mean "That kid is cute!"

She told me, however, ”激かわ” or "超かわ" is acceptable to mean "very cute." Not formal though.

I asked my Japanese teacher this at some point, and she told me kawa by itself is very informal, kawaii is the full version of the word. Not that I have any first hand experience in how you would use kawa.