Are the hamsters showing signs of illness like wet tail? Although that's not usually transferable to humans, as far as I know.
Have you aired your home? Open windows and doors and get some fresh air into the house. Get everyone outside, even the sick person, to get some fresh air into the lungs. Flush the germs out of the house. Wash down surfaces and laundry and toys. Make sure that those who are able to eat are eating healthfully and avoiding junk food and sugary snacks and drinks. Stay well rested.
And try to avoid staying cooped up in the house, so those not requiring rest should be active and out of the house getting fresh air. Even if it's chilly outside, especially when it's chilly and cold since the cold air kills germs.
Hot teas like chai tea have some great healing spices in them. You don't even have to add milk. Add local honey to sweeten and it's good to go.