Base Burn! Ouch - as a chemist we use Codium Hydroxide in the lab all the time. Always careful and were gloves and goggles. Strong Acids or Bases are both dangerous and destroy tissue. Baking soda probally didn't too much but the vinegar should neutralize it.
I'm praying for a speedy recovery. I lost a toe nail when I bounced a big chuck of fire wood off my bare big toe while standing on concrtete. Took nearly a year to grow back and was really tender that whole time.