Piston stuck in caliper after rear brakes replaced

I recently had my rear brakes replaced. The whole works. The next day, my car started squeaking very loudly (wasn't doing that before) and also smelling burnt coming from the rear tires. I called the mechanic and he told me to drive it for at least 100 miles to "break them in". The problem seemed to only get worse, coming mostly from back left side. I brought it in about two weeks later and it was discovered that there was a piston stuck in the caliper on the back left side. I had just paid $400.00 for everything he did to the rear brakes (pads, etc.). Now he is quoting me another $350.00 plus the cost of a rental car for the day. I feel as though this problem was a direct result of his work on the brakes. The problems started the following day and further, he told me to keep driving on them. My question being that, since this issue occurred only after new brakes were put on, shouldn't they fix this piston problem for free? Or am I way off base here? Any advice here is welcomed and would be greatly appreciated!
Sincerely,
Single mother of three not willing to pay this guy $800.00 for rear brakes.