There aren't any govt programs for such. Unfortunately, cars are not considered necessities even though you have to get to doctor's appts.
What you can do is apply with your county dept for council on aging. They also help the disabled. Someone from the agency will come out to your house for a face-to-face interview. They approve you relatively quickly (compared to food stamps & medicaid in my area which are also county svcs). Of course, you have to be legally disabled w/documentation & they will walk around your house's interior to determine what services will benefit you. The interviewer is usually a nurse or social worker.
The services they can help you with are volunteers will drive you to doctors appointments, to the grocery, on errands, etc., but u have to let them know well in advance since the program operates on volunteers.
This agency also operate the meals on wheels program to deliver cooked meals to your house if you have difficulty preparing them. However, this program has had so many budget cuts that ppl are having to get fewer deliveries per week.
You see the difference here? This agency provides svcs to enable you to see doctors & be fed. Those things are necessary.
As for donated cars...sometimes a church will donate one. Very few, though & under special circumstances. I only know of 2 instances in the hundreds of disabled ppl I know in 2 states. This particular church was Episcopalian. Ppl are members...they don't just do it for ppl off the street. (Many churches do offer food pantries open to the public, tho. They have a limit on the amt of food you get & how often u get it.)