The details roughly match The Original Series novel "The Vulcan Academy Murders" by Jean Lorrah, published November 1984 (Novel #20 in the TOS series).
Kirk and the Enterprise travel to Vulcan to allow an injured crew member (Remington) to participate in an experimental procedure to repair nerve damage, only to find Spock's mother Amanda is also undergoing the same technique. During their stay, a number of attempts at sabotage are made, resulting in a fire at the academy, during which Kirk sustains some burns, but is healed up over night. The following day (Chapter 21), Kirk considers the sonic shower in this way:
If it had been actual sunburn, he would have awakened the next day with an a golden tan. As it was, he saw, dry skin was already flaking in patches off his arms, where the blisters had been. Well, a sonic shower would rid him of the terminal-dandruff effect.
Just after this passage is the return of Eleyna Miller, a human female science student at the Vulcan Academy of Science, and assistant to Sarek in his advanced programming course. She also features as the love interest for Kirk, here addressing him while he is wearing a "one-size-fits-all" pants and tunic work-out outfit:
Eleyna returned. "Ready to go? You know, you really do look good in anything, Jim."