Will Allah punish me for taunting someone who frequently taunted me about a physical flaw they were born with, knowing that I did not initiate the taunting?

It is impermissible to shame a Muslim for a physical defect. If you shamed someone with the same thing they shamed you with, and you did not exceed the Sharia-ordained limits, then there is no blame upon you. However, if you exaggerated in shaming them to the extent that the person was severely harmed, then you are obliged to repent, and part of perfecting repentance is to seek their forgiveness for your transgression.