She should look at this as an opportunity. Get the NCIS scripwriters to come up with a plot in which she is attacked and ends up in the hospital. Use some CGI cosmetics to give her something like her usual look.
When Edward Woodward had a heart attack during mid-season production of popular show The Equalizer, they initially wrote him out of the script by writing that he had been kidnapped. When he was still mostly bedridden, they did a rescue scene in which he was carried around on a stretcher for a short distance, to conclude the two or three parter.
More to the point, when shooting the original Star Trek show, William Shatner was stung by a wasp on the eyelid, and they had to be very crafty, and use a ton of makeup, to hide it.
I thought Kirk was allergic to Tribble dander.