That can happen with all kinds of "odd" movements, that is, moving in an unfamiliar way. Some people get it just from bending over the sink to spit out their toothpaste. So if you were bending over and scrubbing a toilet or leaning into the tub to do the tile, that's often enough to strain something. Aside from what you were doing when it occurred, what had you been doing in the days before it? For example, shoveling snow and raking it off roofs (which we've been doing plenty of) can use muscles in an odd way.
If you've been coughing, absolutely that can stress out the muscles in that area, and then some ordinary favoring of what is sore can cause you to strain something else. It doesn't take much to inflame the disks in the back and have them irritate all the nerves that emanate from there, referring pain to other areas (shoulder blades, lower back and down the leg, etc.)
The best thing when it first happens is ice, not heat. The back and shoulders are tough to get to because you use them just to position yourself against an ice pack, but it's the best thing. Don't use heat - as soothing as it may seem - because it increase inflammation.