I called my landlord to let him know and he told me where to find de-clogging stuff in the basement. (He then called me back to confirm I knew where in the basement to find it. I resisted saying "I've known this building longer than you have.") Took several treatments, but as I hadn't treated it at all for way too long, the treatments were likely needed. Test shower happened later, with me being careful that stuff didn't back up. So far, so good. *is watchful and stuff*
Thanks to previously imparted knowledge, I also took care of some gunk or junk or some other form of "unk" that was in my shower head, and that works better, too. *is more accomplished and stuff*
End result: I'm properly showered for the first time in, um, a little too long. *is clean and scrubbed and stuff* You probably don't want to know how I cleaned myself during the days when the showered was clogged. I'd wash my hair and my upper parts in the kitchen sink, which is the biggest sink in the apartment. I, um, er, well, also washed my lower parts by filling a large bowl with water, hovering over the toilet, wetting the particular lower parts, soaping them up, then rinsing with more water from the bowl. Awkward. And, I know: SEXY.
Thus ends a period of kinda-sorta camping in my own apartment. And thus begins a period of being more vigilant about how my pipes are working!