Sorry, no. You can't take a medical expense deduction for someone who is not a dependent, and you can't take a charity expense deduction for providing service to a specific individual, even if that person is needy.
On the other hand, if you volunteered with a registered charity to drive needy people to appointments, those miles could be deducted at the charitable mileage rate of 17 cents per mile. But the charity would have to schedule your rides. If you choose to provide the service to a specific person, that's not deductible.
