Which type of contractor to contact for leaking balcony floor?

I have a small balcony attached to my 2nd floor bedroom that is leaking. The floor of the balcony has a small drain which runs down and across to the downspout. Beneath the balcony is my living room. I have removed small of the ceiling drywall where the water is and appears the drain plumbing is fine (pour water down it, no leak). Leak seems to come from outside the drain and the balcony subfloor is very wet with some rot. What contractor should I be looking for? A roofer? A waterproofer? If I were to get this fixed, what is the best way to waterproof and drain water for a balcony?