As a female, it can be both flattering and embarrassing. If I'm with close friends then it's kinda flattering because my friends and I will joke about it afterwards. But if I'm with people I hardly know I might be a little embarrassed.
You might do something to show them you are a real person instead of an image, sounds like that person is centered on "looks" and not substance , Id feel better if they said "hey , I like your personality". Even if I was really that good looking !