One of the "correct answers" is " I do not have appointment with the doctor this week." It should be " I do not have an appointment with the doctor this week."
In mid-Atlantic U. S. we would say, "I don't have a doctor's appointment this week." (Yes, we use the possesive, "doctor's.")
There is no "any" in this phrase. I think it should read: "I do not have a doctor appointment this week". The article is needed in English
A cause for mild celebration by Medicare folk.