I'm in the "see the doctor" camp. I detoxed at home but it wasn't pleasant and it isn't recommended.
It really isn't fair to your parents to put them in charge of sustaining your addiction until you're ready to take time off. Detoxing only takes a few days--three days to a week, depending. With some medical help/monitoring you might only have to miss a couple of days of work. You can still do in-patient to get on really solid ground in a few weeks. In the meantime, you could attend AA meetings and get support here.