How is HCV transmitted?
HCV is transmitted primarily through large or repeated percutaneous (i.e., passage through the skin) exposures to infectious blood, such as
Injection drug use (currently the most common means of HCV transmission in the United States)
Receipt of donated blood, blood products, and organs (once a common means of transmission but now rare in the United States since blood screening became available in 1992)
Needlestick injuries in health care settings
Birth to an HCV-infected mother
HCV can also be spread infrequently through
Sex with an HCV-infected person (an inefficient means of transmission)
Sharing personal items contaminated with infectious blood, such as razors or toothbrushes (also inefficient vectors of transmission)
Other health care procedures that involve invasive procedures, such as injections (usually recognized in the context of outbreaks)
http://www.cdc.gov/hepatitis/hcv/hcvfaq.htm
Also, my above comments about getting an antibodies test would equally apply to HBV. The risk of transmission from the scenario that you described would be just as unlikely.
does your relative have HCV? if not, then no risk of contracting HCV from her. Presumably, the hospital where your relative is admitted does a good job of cleaning its facilities in order to minimize risk of transmission of any infectious agents to patients or visitors, too.
You can web search for methods of transmission of hepatitis C. From what you have described, if your relative were infected, I believe the risk of transmission would be very very very low. However, in about a month or so, if you are still concerned, you could always ask your family physician to order up a HCV antibodies blood test for you and proceed from there.