"My younger brother is not only tall, but also good-looking."
I believe 好看 is more related to clothes. Hat, dresses, shirts... can be 好看. Someone is 好看 when you refer to the way that person is dressed: You look good (in that suit). 帅 means handsome or good-looking at all times, it refers to your face, body, height...
Should很be added in front of高? 帥Has it but English didn't specify very, inormally use很 or 好 in front of these kind of words