I found the ultrasound treatment from the physio very helpful with this problem.
So was feeding lying down, and sometimes expressing so that someone else could do the feeding. Ibuprofen is safe to use while breastfeeding, and helped with the swelling and pain.

It has become easier in the last couple of months as bub is less floppy and easier to handle.
I lie him partly across my lap, almost like he is sitting beside me - that way my arms don't take any weight.

If you are in Victoria, write to the arthritis foundation for a copy of "juggling sore joints and babies" - heaps of useful tips.

Stopping feeding won't help you that much - you still have a lot of baby handling to do. The huge help is that in the next month or so you shouldn't have to support her head anywhere near as much, and the strain on your wrists decreases lots - I have much less wrist pain from my 6.5 kg 4 month old compared to when he was a 3kg newbie.