What is the difference between turgid, tumid, and tumescent?

Tumid and turgid appear to be very similar in meaning both etymologically and in modern usage, but to my ears and by association with tumor, tumid carries a more negative, serious connotation, while turgid is a swelling but not necessarily diseased in itself. As @Nate notes in the comments, turgid is used positively in biology. (These are my impressions. Take them cum grano salis.)

Etymologically, tumid meant "morbidly swollen", i.e., swollen because of disease, and is cognate to tumor. Turgid also meant "to swell" and originated in medical contexts. The Latin roots of these words (tumere, turgere) also marks them as being very close in meaning if not synonymous in many contexts, with tumere appearing to be more common in classical Latin.

Tumescent is also cognate with tumid. The "sc" in the middle of Latinate words typically indicates a changing state, e.g., fluorescent, condescend, convalescing, adolescent, effervescent, emasculate, etc. (Note this doesn't apply to prefixes that make the letter combination by happenstance, e.g., discombobulate, disconnect, misconstrue, resuscitation, etc.; to compound words where the "sc" was at the beginning of one of the pieces, e.g., kaleidoscope, subscribe; or to words from Greek or other languages, e.g., proboscis.) Here it makes the meaning progressive rather than tumid's static sense: swelling rather than swelled.