Just had back brakes and rotors replaced a week ago, came home from church yesterday and there was this horrible smell and smoke coming from passenger side back brake area what could me the cause for this. Can I drive it at least back to the place that fixed it?
Sounds to me like you have a stuck caliper. Basically this means that your brake pad is stuck pressing on your rotor just like if you had your foot on the brake pedal constantly. This causes a lot of friction which leads to overheated brakes and the lovely odor that accompanies it.
The place that did your brakes probably forgot to clean or lube some parts in your caliper or just put it back together wrong. You may be lucky enough that it will free itself up and it will work just fine again, but there is no guarantee it will stay that way. Take it back to them and have them fix it.
As far as driving it there goes, I would not. Overheated brakes can heat up the brake fluid in your lines and potentially boil it. If it boils, you lose your ability to brake at all (except with the hand brake). I would not risk driving a car that I couldn't stop. Call the shop and explain to them what is going on and get them to tow it or pay for a tow. They can't expect you to drive a death trap back to them.
A few years ago I had replaced my rear brakes with ceramic pads and new rotors. Later that day I was driving out of town and noticed exactly what you are describing. I pulled over to the side and pulled the rear tire off to see what the problem was, thinking it was a stuck caliper or something. When I got it off, I noticed there was nothing wrong. Nothing was dragging, the smoke had stopped, and all was well. I don't know if this is your exact case, but would bet it probably is. Drive the car back to the place where you had it done and have them inspect it for you. I will bet there is nothing wrong, but it doesn't hurt to have it reinspected.
My first thought is that they didn't adjust the pistons or emergency brake mechanism properly. If you jack the car up, can you freely turn the wheel, or is it stuck?
Did you have a brake flush done when your brakes were serviced? If not you smoked a caliper. I'm assuming it is disc brakes system. If the pads were worn very thin the piston in the caliper will sometimes stick and not return. I've seen it a few times and usually it's from moisture in the brake fluid. It will be black or green which is bad! Normal fluid is Amber in color. Brake fluid flush is very important. Keeps everything working properly. Heat from the pads get absorbed into the line and boils the water causing etching of the piston and then it hangs up. I'd have it towed in. If the rotor is that hit you will need a new one and a caliper and if it's a rear wheel drive the axle seal will need to be replaced. It happens they should correct it at your cost of the caliper. Which you should do both sides and the flex line as well and flush the brake system.