It may be that the reason for your sister's behavior is because she is afraid of germs, also called mysophobia. It is actually common that mysophobia starts to manifest in teenage years, and for most people it goes away by itself (see note below). Other symptoms for mysophobia are:
- Compulsive hand washing
- Excessive use of disinfectants and antibacterial soap
- Fear of physical contact with others
- Extreme fear of getting sick
- Reacting with extreme fear to media reports of new diseases
- Fear of certain locations, such as doctor’s offices and
airplanes, where germs or sick people might be present or confined (source)
Does your sister manifest any of the above, besides compulsive hand washing? Is the hand washing severely impacting her everyday life?
As other wrote, it is by definition hard to reason with somebody who has a irrational fear. Nevertheless, there might be some steps to take at home before deciding to take her to a (mental health) professional.
Step 1. Educate the child on how to protect herself against germs.
Step 2. Provide the child with control over germs. Give him the steps he can take to reduce his chances of being harmed by germs. Teach him how to eat healthy by consuming items such as fruits, vegetable, whole grains and lean proteins. Help him get regular exercise. Teach him about how exercise builds his immune system's ability to fight off any unwanted germs.
Step 3. Have the child talk to a mental health professional who specializes in exposure therapy. According to HelpGuide.org, exposure therapy is done by exposing the child within a safe and controlled environment to the situations or objects she fears. The exposures will usually happen over time and will build up in intensity as the child is able to handle more.
Note: I recently read an article about common fears or phobias by age. I will try to find the source and add it later.