I have never had a baby but a friend of mine had similar problems although didnt have implants didnt breast feed and had very painful swollen breasts. She was recommended to wrap bandages tightly around breasts each day and take off during night- maybe best to consult your midwife though
Because you're not breastfeeding (which would get rid of the pressure most wonderfully, in addition to quite a few other benefits) you just have to wait for it to go down on it's own. This can take a few months or a few weeks. It varies for each female. Do NOT pump or squeeze any out because you'll make it worse. Wrap something tight around your chest, and you can also use cabbage leaves in your bra to help try and reduce it.