Other Picking up things from other rodant?

Yes mice can get pet rodents sick. I would disinfect as much of the house as possible and make sure to get rid of any urine or droppings the mouse might have left behind. Check all food containers and places food is stored since they are quite adept at getting into cereals and other tasty food items. If there's any chance a mouse got into the hamster food throw it out and get a new container otherwise wash the outside of the current container. Then just keep the hamster cage extra clean so the hamster isn't exposed to anything else that might stress her immune system. Keep an eye on her for a week or 2 to make sure she doesn't get sick with anything from her escape. If she has soft droppings, runny nose or eyes, is less active, has trouble breathing, or is sneezing/coughing then take her to the vet right away. Living on a farm we've had mice show up quite frequently and never had anyone get sick so she will probably be fine but there is a chance so it's good to take precautions.