I occasionally have that problem because my index finger nail is grown out a little bit for classical technique.  So when I play electric with a pick the index finger nail can sometimes get snagged on a string!  The solution for me is a lighter pick touch.  Just backing off a bit, stop digging too hard with the pick solves it.

You also might try slightly thicker or heavier picks.  And of course try to choke up a bit less on the pick.

In my experience it's the side of the thumb that helps with harmonics & certain muting.  So keeping my index finger out of the way is never a problem for tone creation.

You might try a small piece of athletic tape instead of a Band-Aid.  Or you could try some clear nail polish or hardener.  But I think your best bet is improved technique.

Hope that helps!