This advice is based on personal experience and is not medical advice.
I personally wouldn't feel that the risk was any higher while breastfeeding. You wouldn't have to worry about bleeding like you would during pregnancy.
It probably will hurt when you try to fall asleep, but I know that mine didn't keep me awake. If you're very sensitive to pain, you may want to consider the timing of getting it done. There's no reason to remove it once it's healed, especially when it's first healed because it can still close up enough to make it hard to get the piercing back in.
While it's healing, I would try to avoid the pool, especially with kids. You may not mean to dunk your head, but you can get splashed or slip. It isn't horrible to accidentally get some pool water on it, but it's not ideal.