Not cleaning the house and constantly coughing

My roommate and I are living in the same apartment, but honestly, we are very different when it comes to hygiene. He is constantly coughing, has a runny nose, and acts like he’s sick, but he never wants to clean up or tidy the place. I’ve been patiently cleaning for a week, while he just lounges on the couch and rests. I don’t want to invade his personal space, but I wonder if he should see a doctor. Do you think I should explain my situation and ask him to participate in the cleaning routine, or should I question his health?