Never lie to your medical caretakers. They make decisions based on your information, and if the information is not accurate, you might not get the right treatment.
One of the best places to catch a vaccine-preventable disease in in the ER. When a Swiss tourist had measles in Tucson, they had to go through all the medical records of people who were in the ER with her and contact the unvaccinated ones for followup and to let them knoe to watch closely for symptoms.
NOTE: An infant who was in an ER room across the hall from the tourist for 45 minutes was hospitalized later (peds ICU) for measles pneumonia. It's that contagious.