I finally broke down and went to an allergist.
It was a pretty fascinating experience. The nurse first poked me with two plastic sticks that inoculated me with a positive and negative control (to confirm that taking OTC medicine a few days earlier wouldn't interfere with the test). After a few minutes, the 6-spotted poke-mark on the positive side rose up like a skeeter bite.
She then brought in two racks with dozens of little plastic pokers sitting in vials of colored extracts. Each extract contained a label such as "oak" or "alternaria." All together, there were dozens of individual preparations of different tree, wildflower and grass pollens, fungal spores and animal dander. She laid down three rows of pokes on my left arm of our most common local allergens and left me to react.
Soon after, I became aware of a building itching sensation over one of the central pokes, eventually accompanied by lesser itches by my wrist and elbow. When the doctor returned, two large puffy bumps had swelled in the middle of my forearm, with lesser bumps around it. The two most prominent bumps were due to two kinds of dust mites, and the smaller ones, cat dander and the pollen of timothy (a common pasture grass)!
I left with a prescription and a better sense of how to lessen my exposure to dust mites.