You have (6) 100w bulbs in a closet

That's 5a right there = 1/3 of the power on the circuit
Are you sure they are rated for 100w bulbs? Usually (2) 60w bulbs
Install 23w CFL's in place of the 100w bulbs
Install 9w CFL's in place of the 40w bulbs
That will free up 539w+248w = 787w
Plus save on your electric bill
The lights alone are using 1/2 of the circuit power
As stated the bathroom should have a dedicated 20a circuit
Poccibly the bathroomdoes & this is a dressing area?
Poor choice on the electricians part to mix all the lights & outlets
He should run a new circuit