I don't know that one would necessarily say "My, you are beautiful in profile!" as a common complement (that would be a very specific, flattering thing to say, or creepy, depending on the context!), but a beautiful profile is definitely a thing in English. It's a little poetic.
Does it mean, "you have a beautiful figure"? I've never heard profile used like this... and I've lived in 3 English speaking countries as well as being British myself. It seems very unnatural and almost insulting or maybe even creepy. I automatically assumed it was referencing an online profile, which would make it even more insulting. Lol