what is America's best girl singer?

Beth Hart. She mostly tours outside the U.S. which is why few Americans have heard of her.
https://www.youtube.com/watch?v=J5_G6A28uYs
https://youtu.be/DEFlTtz0Fy0?t=59

it is .............. taylor swift or beyonce?

lana del rey

Personally, my favorite female singer (at least, from America) is Jenny Lewis.

'Im sure you meant WHO not WHAT. There is no such animal. People can only state who they like best, but no one can name anyone as the best singer in America or anywhere else.

Boy George