Is It Possible to Reduce a Protruding Upper Lip Tubercle?

I am a 27 yr old woman. The "tubercle" on my upper lip is quite droopy looking and it's always annoyed me. It looks like a the way a baby's lips look. I was wondering if a bit of flesh could be removed and then a few stitches done to flatten that part of my lips? Is this a common procedure? What kind of doctor should do it? I also feel I could benefit from injections on my upper lip to make it more equal to my bottom lips (in size). Thank you for your feedback!