There's only 1 mission where your settlers are sick at the start, so you'll probably have to play as the healer knight for that one. But other than that mission, you can play as any of the knights, because your settlers only get sick when your city population gets to 150. Before that happens, you should build 1 or 2 herb-gatherer huts near the herb patches, and build 1 or 2 pharmacies in the city centre to convert the herbs to medicine. Any sick settlers will then go to the nearest pharmacy and heal themselves, so the healer knight isn't needed. Are you sure that they're sick, and not on strike about something else?
All times are (GMT -08:00) Pacific Time (US & Canada). Current time is 1:26:19 AM