Yup, sounds normal to me too. We have a mixture of 20 or so Tiger Barbs: Standard, Green and Albino and they go through spells of chasing and "fighting" with each other.
I've never seen the nipping turn into anything more aggressive and they don't seem to damage themselves.
I've seen smaller numbers (less than 3 in total) of Tiger Barbs being very aggressive to each other - but that was because they were fighting to dominate each other in such a small group.
Alys