Which type of doctor specializes in tailbone pain for teenagers?

Orthopedist: Of course it depends on what you mean by "tailbone pain". But chronic lower back pain usually is an orthopedist's domain. Sometimes there can be nerve pinching or a tethered cord, mild spina bifida, etc, but those are rare. Start with your regular doc, to rule out infection or nerve issue, then likely on to the orthopedist.

Agree with Dr Amster: However, if the cause of the pain is that the teenager bruised it by falling on it, bumping it etc., and they are otherwise fine and able to go about their business unimpeded, then time will heal it. If the cause is that s/he sits on it extensively, then the solution is to get up and move. In either case a surgeon is unnecessary.