Leo- When you're sick you usually curl up in bed and read, he's always good to come visit you and bring you hot tea, or water since he knows you don't drink a lot when you're sick. Sometime's he'll read to you and let you sleep. He always plays with your hair and makes sure that you are comfortable.
Raph- He knows that you don't like to admit that you are sick, so he'll suggest doing things that help you out, like watching a movie at home, or snuggling under the covers. When you get really sick he likes to do small things for you, like getting you water, or gently massaging your back. He's always down for cuddling, even if it means he might get sick.
Donnie- He goes a little overboard when you're sick, even with a sniffle, he tucks you in bed and takes your temperature every hour on the hour. He brings you water and gives you smooches and plays with your hands and tries to get you to fall asleep by reading lectures from his favorite people, but this mostly causes you to get to excited about whatever he is talking about, and then you can't sleep. The only way Donnie can get you to fall asleep is by climbing into bed with you and telling you old stories that Splinter used to tell the boys about Ninja's in Japan.
Mikey- He likes to assume the role of a mother hen when you're sick. He fusses over you and brings you chicken noodle soup, and tucks you in and makes you cozy. He brings you his favorite comics to read and puts cool wash cloths on your head, and insists on doing everything for you. He doesn't get to take care of people often, and when he does he goes all out.