I personally feel that birth marks are a part of our uniqueness and should be celebrated. With that being said though, I understand that many birthmarks are socially hard to accept, even if we have the best self confidence.
The hard part though, is with the birthmark being on your face. There is a lot at stake if you choose to go with any surgical methods. Instead, I would consider using some complexion equalizer cosmetics or something that can help blend the color of your birthmark with the color of the rest of your skin.
If nothing else, you could get a very cool face tattoo =)