No. Hepatitis and HIV are not transferred through casual contact. In order to contract either of these diseases, you would need to be exposed to blood or body fluids that contain the virus. The preamble has to be that the person cleaning your face has HIV or Hepatitis C. Even if the person has it, the risk of transmission from what you described is extremely low
There is a very small chance of contracting hepatitis or HIV if you are in close contact with someone who is infected and has an open wound, but it is much more likely that you will contract another illness such as the flu. It is important to practice safe sex and always use protection when having sex with someone who may be at risk for contracting one of these diseases.
If you are still worried, you may want to consider getting blood test done to exclude infection.