Unless you have someone who is a legal guardian of you that is allowed to make decisions on your behalf then no a doctor nor anyone else can force a person into a nursing home or assisted living facility.
As an adult you have the right to stay where you want to stay and cannot be forced against your will into a nursing home.
The only exception is that if you need to go to a mental health facility because you're a threat to yourself or others then you can be temporarily held involuntarily for up to 72 hours.
After 72 hours the mental health facility has to get a judges order to hold you longer and if they don't then they have to legally release you.
But just for a regular nursing home they cannot force you into one against your will.