Here's how to bathe when your left arm doesn't work, but your hand does: bring everything into range of your hand, rather than bringing your hand into range.
In other words, to scrub your left armpit, you must first firmly grasp your left wrist in your right hand. Then you must lever your left arm into such a position that it stays propped behind your head. Then you scrub and rinse.
To wash your hair, you must lower your head to the level at which both hands can reach it. (Scrubbing one-handed is not an option. I have a lot of hair.) Similarly, if you wish to put your wet hair up in a clip to keep it from falling in your face and making you homicidal, you must bend over to the point that your arm won't fall down when you're trying to use your hand. This is especially important if the distal portion of your arm (ie, your hand and wrist) are unaffected by the weakness in your shoulder and tricep. If your arm starts to drop, you will instinctively tighten your grip on your own hair, demonstrating exactly how heavy your arm is. Owie.
Getting into a bra was a whole new kind of humbling experience. I did not know it was possible to simultaneously hold open the arm strap of a bra while using the same hand to lever my left elbow through said strap.
Now all I want to do is take a nap.