Recently I strained my wrist quite badly while climbing. Slopers and pinches are painful. I’m concerned about pushing it too hard to the point of tearing cartilage. I just feel that most doctors, no matter how you explain it to them, don’t understand climbing at all.
Julian Assange would have a better chance of perusing CIA documents in the national archive than doctors have of finding any research about climbing injuries. In this instance, however, knowledge of climbing injuries is not especially necessary, and both the chiro and PT have given you sound advice.
Based on your description, it sounds like you ruptured the radio-ulna ligament and have developed radial-ulna joint instability. The lump you describe is the now-unrestrained ulna sticking out the side. Don’t worry too much about injuring the triangular fibrocartilage complex (TFC) that sits between the ulna and the carpal bones on that side—you already have!
Taping the wrist will work reasonably well. However, increasing stability by way of compression is about as rudimentary as the well-known prosthesis of Captain James Hook. The ulna-side carpal bones will tend to drift forward, primarily because you will have instability resulting from damaged ligaments and the probable disruption to the TFC complex. This disc contributes significantly to stability on the little-finger side of your wrist.
Slopers will hurt because the mechanics of your wrist now operate much like a bunch of coins in a tumble dryer. Pinches will hurt because your wrist is typically flexed to the little-finger side, exerting direct stress on the injured structures, especially the TFC complex. Surgery is still an option, but most surgeons are loath to do it because it is both difficult and prone to failure. My concern with taping is that it may not provide sufficient stability to prevent further degeneration of the TFC complex and carpal joints, resulting in significant arthritic degeneration down the line. Hand specialist. MRI. Many factors will determine the best course of action, not least of all the extent of damage.