Each breast will respond a bit differently to implants. One may hurt more than the other. If the breasts are markedly different in size then I would be concerned with a hematoma. Best to always review with your surgeon.
You know, for a submuscular breast augmentation, the left side is really the more unusual with no swelling or discomfort this soon out from surgery. I often see asymmetry in healing and swelling after breast augmentation and most of the time it evens out given a few weeks for the slow side to catch up to the "fast healing" side. That being said, rarely it is due to bleeding around the implant or fluid, and if that is the case, the right side should seem larger than the left as well. If you were my patient I would want to see you to make sure there was not a problem. And your surgeon can tell by exam if it's just swelling which will resolve on its own, or if there is a problem that needs to be addressed. If both sides would just behave the same way it would save a great many women a lot of worry, but they usually differ, at least a little. Good luck!
There are a number of different reasons that could explain this, if you are right handed and stronger on that side it will be more painful because you have to cut through a bigger muscle or you could have a fluid collection and possible a bleed though likely small. I would suggest icing and using your meds!