JC had a severe reaction to his first booster shot - vomiting and a fever, so now our vet uses a different brand and gives him a shot against allergic reactions. That's probably not necessary if it's a mild reaction like lethargy, but I would remind the vet of the reaction the next time the cat needs a booster. I have a list of reactions from the "ASPCA Complete Guide to Cats":
Mild reactions (fairly common, appearing within hours to several days after vaccinations, should last no more than several days): discomfort at vaccination site, mild fever, diminished activity and appetite, sneezing about 4 to 7 days after an intranasal vaccine, development of a small, firm, nonpainful swelling under the skin at the vaccination site, which should disappear after several weeks.
Serious reactions (very rare): serious and potentially life-threatening allergic reaction within several minutes to an hour after vaccination, manifested as hives, severe vomiting and diarrhea, and/or collapse and death; a kind of tumor (sarcoma), developing at the vaccine site several weeks, months or even longer after vaccination.
Many vets now give vaccinations in the extremities only because of the risk of sarcomas. That way, the leg can be amputated to save the cat's life.