A) I am going to see a doctor.
B) I am going to see the doctor.
C) I am going to the doctor.
D) I am going to the doctor's office.
E) I am going to the doctor's.
F) I am going to see my doctor.
G) I am going to see a new doctor.
Choice A does not mean a random doctor. It simply does not say (in this sentence) what doctor. Usually the speaker is talking about the disease or problem, and is not interested in talking about "which doctor I will use".
Choice B,C,D,E do not mean "my regular doctor". The phrase "the doctor's" is a standard idiom, which can mean any doctor's office. Many people use clinics, where they do not know what doctor they will see. They still say they are going to "the doctor".
Only choices F and G tell us if the doctor you are visiting is your regular doctor, or a stranger.
Neither H nor J says anything about what doctor you are visiting:
H) Sorry, I can't talk right now. I am at a doctor's office.➡️doesn't use the idiom "the doctor's" so you need office
J) Sorry, I can't talk right now. I am at the doctor's ➡️. uses the idiom