It will heal if he can be isolated, but as you wilder said, you need to find out why it was nipped in the 1st place. The common cause with tiger barbs, is not enough of them. The more of them there is, the more the aggression is spread out. This way one barb will not be singled out, and continually bullied. make sure you have sufficient tank capacity before you think about adding more, and obviously, check the water perams.
On the number game front, i would suggest 6 as an absolute minimum of tigers, but even 6 can cause problems.. general feeling is that the omptimum number is 8. More is better still, but your looking at a lot of space for 10 or more adult, fully grown barbs... they like to swim!