What do you mean by embarrassing?
Embarrassing for Rand? I think she is thinking that she's within 48 hours of death and embarrasment is not something that still has room left. She may never have expressed any feeling about wanting to attract Kirk in normal circumstances, but dying and being mentally impared could make buried feelings surface. I thought it was well done as Captain Kirk and Janice were trying to cope with their own relationships, personal and professional, and dealing with them both coming to an abrupt end, because they were nearly dead.
That's an in-story rationalization, but metatextually, it just feels like another instance of the writers reducing Rand to a sexually submissive doormat who was more concerned with being attractive to her male employer than with being good at her job. Which is perfectly consistent with how most working women were written in the 1960s -- just working until they could succeed in attracting a husband, whereupon they'd happily retire to homemaking and motherhood -- but it's hardly the progressiveness we'd like to see in
Star Trek. Combined with Rand's "If the Captain wanted to rape me, I guess it'd be okay" attitude in "The Enemy Within," it adds up to make her a very conventional, backward portrayal of a female character and just leaves me with a sour taste.