Sounds like you have what we call a partial nail removal with phenolization (or another acid such as sodium hydroxide). Assuming that it was done properly and the acid applied for the recommended length of time, then this is probably just a simple "regrowth".
On a rare occasion they regrow for no known reason even though the acid technique is supposed to be permanent. No one seems to know why, they just seem to happen sometimes. I get 1 or 2 every few years or so.
Most of those I have seen that regrow and if they are painful, I just do them again and none have regrown a second time.
Might pay to go back to the dr and see what they say might have happened.