She has 5 headphones but she does not like to share even though we live under the same roof.
That kind of person is - stingy. http://www.dictionary.com/browse/stingy https://www.collinsdictionary.com/dictionary/english/stingy
An apt term would be penurious. As the second definition in Merriam-Webster's dictionary shows:
2 : given to or marked by extreme stinting frugality (https://www.merriam-webster.com/dictionary/penurious).
However, the example given could be more a case where the person in question is simply paranoid, or 'grossed out', by the prospect of someone else's hair/oils/DNA what have you being in contact with their own ears after usage.
- Serving one's own interests, especially without concern for the needs or interests of others.
- Exhibiting concern solely for one's own interests