Re: Nursing one side at a time
As long as you nurse on demand, your supply will eventually level off to your baby's needs whether she is nursing on one breast at a time or both. If one is no longer enough, then she will take the other. I nursed on only one side for about 7 months, at which point my son started taking both sides. He gained a lot of weight throughout his infancy, and I have never had any problems with low supply.
It is really variable how long the discomfort can last. It resolves pretty quickly for some mamas, it takes much longer for others. I had really painful engorgement for about 3 months. It improved after that, but I still had an oversupply until sometime around 6 months (although it wasn't as problematic after 3 months). But that's just me; everyone is different.
The best thing to do is to stay the course and nurse on demand. You can continue to offer the other breast to see if your baby will take it, but she might not and that's okay. The full feeling will eventually go away (and that is not a bad thing - it means that your body is matching your baby's needs). I used cold compresses when the engorgement was unbearably painful. Cabbage leaves are supposed to work well too.
K. Sophia - Mama to my little lactivore, the amazing Mr. X (11/10).