Is MRSA only a problem in hospitals for sick people?

No. Anyone can be infected with mrsa, it use be that MRSA was acquired in the hospital, but now MRSA is increasingly acquired in the community.
MRSA. Mrsa is a problem for everyone whether in a hospital or not. It is difficult to treat and is developing more and more resistance to the new antibiotics that are being used to treat it. Overuse of all antibiotics have lead to this problem and everyone needs to understand that the more they demand antibiotics for infections that are most likely viral only add to this problem for the future.
No in community. Community acquired MRSA is spread by direct contact with a person with a CA-MRSA infection (e.g., a draining boil) or an object used by that person (e.g., sports equipment, clothes, towels, razors, etc.) Crowded living conditions and poor hygiene are main causes for spreading the disease.
Mrsa in community. Mrsa is often more severe in the hospital. There are community types of Mrsa outside hospitals. It is often passed skin it skin with athletes, closely related family.