There are three common ways for disc brakes to stick, and what you were experiencing is definitely symptomatic of stuck brakes.
- The caliper slides might be rusted
- The piston in the caliper is getting crooked in the bore and not retracting
- The brake hose has collapsed internally and is not releasing pressure
The easiest thing to inspect is the pins, but stuck pins usually just lead to uneven or crooked wear on brake pads. Still if the caliper frame does not slide on the pins they should be replaced (provided they are replaceable).
Any time I have a problem with a stuck caliper and the pins are ruled out I first disconnect the hose from the caliper and try to retract the piston with a C-clamp. There should be little to no resistance, and if there is then the caliper piston is sticking. It's best to replace the caliper if this is the problem.
If the piston retracts easily, then the brake hose should be replaced. With the symptoms you're describing this is my first suspicion.
The squealing could be a symptom of your stuck brakes, but could also be the wear tab on your pads. After smoking as much as you described I would be surprised if the pads had any material left on them.
Finally, with what happened to your brakes, it is probably a good idea to replace the brake pads. Because the rotor was probably overheated and then clamped in a single spot with the pads, there's a good chance that a hard spot developed, which will lead to surface runout which you will feel as a pulsing when braking. Because of this, if you're going to have everything apart anyway you should probably replace the rotors.