Sore throat was the worst aftereffect of my surgery. My throat was damaged by the intubation and was not only extremely painful but a serious obstacle to breathing and eating.
So I really sympathize with your current situation.
I got my sore throat under control first with Tylox, a pain killer! The morphine the first two days after surgery did nothing to relieve it. Also, the Cepacol lozenges didn't put a dent in it either. Once I got the pain and discomfort under control, I could progress in breathing and eating so that the antibiotics could keep the sore throat from getting to the point where it sounds like yours is; infection. I pray you didn't pick up any staph from the hospital; those bugs are nasty! And, yes, it can lead to valve damage if not taken care of immediately.
In any case, I would press your doctors to get that under control right away and that should make a huge difference in the rest of your recovery. With heart and sternum wounds to heal, we don't need to be fooling around with stupid problems like sore throats!
I do hope and pray you get relief soon. Keep us posted.