A physician who specializes in treating the elderly is known as a geriatrician.
A geriatrician
gerontology
An oncologist treats people with cancer.
A doctor who treats the elderly (technically defined as any person over the age of 65) is a Geriatrician, or Gerontologist.
a gynecologist
Veterinarians treat animals including cats and dogs.
Cardiologist
Obstetrician
A psychiatrist
ENT specialisd
There isn't a type of doctor who specifically treats doctors.
A Doctor Who treats children is called a paediatrician
If you mean newborns, which I'm guessing you did, the physician responsible for that would be a neonatologist.
A doctor should be called if an elderly or disabled person is constipated for a week or more or if a child seems to be constipated.