Is it common to have pain of the sides of rib after breast reduction?

Yes, it is common. Reduction techniques involve removal of breast tissue down to the margin of the rib cage. The sensory nerves that run from the ribs, to the breasts can be temporarily injured or bruised and the muscles of the chest wall can also be minimally injured. It is not uncommon to have some discomfort on the rib cage for up to four to six weeks after surgery. When this does occur, it is typically very mild. 

Thank you for your question.  Unfortunately your swelling will go up and down.  Three weeks is still early.  Typically you should not start working out until your 6 weeks out.  I suggest you follow all of your doctors post op instructions. Best of luck!Dhaval Patel 
Double Board Certifed
Plastic Surgeon
Chicago
Hoffman Estates
Oakbrook
Orland Park

Check with your PS to be sure nothing unusual is going on, but the 'armpit' side of the breast is commonly the more painful part of the surgery, This is where the sensory nerves enter the surgical area and are irritated.   Additionally, if liposuction was done on the armpit, then the discomfort is usually greater for a few weeks.  Most of this will resolve completely.