I say to continue breastfeeding or pumping to keep your supply renewing itself.
When I was nursing many, many moons ago, I remember several times I thought I was coming down with a cold or the flu only to discover that the fever and other symptoms were caused by my breasts being engorged. Nursing actually made me feel more comfortable and the symptoms went away after the milk was released. That was early on mostly when the kids were about your baby's age, and I would supplement the nursing with pumping the extra to freeze for my anticipated return to work or just to have on hand when needed.
As far as the right side pain goes, I went into a near panic when I was pregnant with my first child over a pain in my right side. I'd had an unexpected pregnancy before her which was a tubal pregnancy resulting in emergency surgery. I was scared to death that I was now experiencing a tubal pregnancy in the right tube which would cause termination of the pregnancy and reduce my ability to conceive since I only had the right tube anyway.
I immediately called the doctor's office. The nurse calmed me telling me that it was probably a round ligament contraction, which was normal.
There are ligaments that connect with your uterus to keep it in position within your body. As your uterus grows, they lengthen to support the pregnancy. After childbirth, they return to a more pre-natal position. So the feeling is a bit like a pulled muscle.
Another factor which I experienced with my second pregnancy constipation. It must have been how she was lying on my insides, because I didn't have a bowel movement for a week after she was born even though they gave me all kinds of stool softeners and laxatives to move things along. Once I started having bowel movements again, I was much more comfortable, but the gas pains can get pretty brutal sometimes.
If you are gassy, simethicone, which is cheap and over-the-counter as a generic, is a good and safe way to relieve the pressure. It's what the doctor would recommend for the baby if it was gassy, too, so it should be safe to take while nursing. Check with the pharmacist first to be sure.
If it's your internal musculature rebounding from the pregnancy, it will pass shortly. Nursing actually helps to tone up the muscles and ligaments, which may be a huge benefit to getting your figure back. You may actually feel the strains when you are nursing.
If you were having a problem with the incision site such as an infection, there would probably be evidence like you'd have with any infected wound. Be sure to keep your post-natal visits with the doctor to see that you are healing from surgery properly. At one month, you should be well on the way to healing unless there are complicating factors such as obesity or diabetes.