You can't be a head of household unless you have a qualifying child dependent and provide more than half the living expenses of your home. (Your parent also can't be head of household if they are living together, by the way. Even though one of them may be the "head" of the household in common terms, the tax filing status means something different.
Each Turbotax Online account can only file one tax return. If you need to file more than one return, you need to create additional accounts. You can have multiple accounts linked to one email address for notifications, just with different user names. You may have logged into your parents account.
