Only your personal income and your personal expenses should be counted. At your first court appearance you will likely be required to fill out a financial declaration form and the court then will decide if you are eligible for representation by the Public Defender.
In the interim, it can't hurt to consult with some local private defense attorneys. Some of them will make themselves available for a free consultation.
Although Mr. Shapiro did not say so I am sure he meant to add that in filling out the financial form include only your income and debts. This could get complicated if you are living at home and not paying rent. Be truthful in your answers. SF is very liberal about appointing the Public Defender but if it turns out later that you didn't really qualify financially you could be made to repay the Public Defender.
You will be required to complete a financial declaration at your first court appearance. Only your income and expenses should be included on the financial declaration. After you complete the financial declaration, the court will determine whether you qualify to be represented by the public defender.
You should advise the court of your financial situation, your net income, your expenses and the fact that your parents will not assist you and that you cannot afford a lawyer on your own. Make it clear to the court even if you need to have a hearing or provide documentation other than the typical petition for a court appointed lawyer.
Depending on the county that you are appearing in - they may not even make an issue out of it - they may just ask - can you afford an attorney and you say no and they appoint the public defender. Some judges make you go out and talk to three lawyers to confirm that you cannot afford it. Your parents income will not be counted.