often, rear callipers are the type that have one piston and have to slide across a bit to bite; usually they jam on not off.
However, dismount calliper and spray with brake cleaner, maybe all it needs short term (but keep an eye on it and check pad wear whilst it's off). Check scored disc too, or if the disc has a pronounced 'lip' at the edge where it didn't get worn but now stops the pads biting. As you had to add fluid, the pads have obviously got thinner, hence the master cylinder went down a bit. That is normal but not all of a sudden - do you check frequently (of course you should) - weekly at least.
Back to swing callipers - do they slide together apart as on oiled silk, or do they not budge? If the latter, they have to come apart and the rods holding the inner to the outer may respond to de-rusting. If the rubber boots covering those parts are even slightly damaged or just a loose fit, that is the probable story.
Twin piston callipers (hydraulic push from both sides, nothing has to slide across) should be near infallible if the pads are OK. Any pad down to bare metal makes a fearful squeal - did that happen lately?
BTW, is the footbrake pedal really really firm now, or a bit squidgy - have you really got all the air out of it?
What colour was the fluid you bled, normally it's darker than when new but if it came out into the jar with crud, you may have a return hole blockage now. Drain whole system overnight, refill gently and re-start the bleed process with all fresh juice.
If you're in the slightest doubt about what you're doing, take it to a pro; it is a killer to have brake failure.