Whether you have spoken to the doctor or not does not * determine the use of 'wants' or 'wanted'.
I think that 'necessarily', injected where I've put the aserisk, may be the operative word. Because having seen the doctor could have some bearing on what is possible.
Potentiality 1:
"My son was transferred to another hospital yesterday. His doctor wants to see me today to give me his opinion. I have to be at the hospital at 2pm."
(The person is telling someone what has been happening, and that he has an appointment with the doctor later on that day."
Potentiality 2:
My son was transferred to another hospital yesterday. His doctor wanted to see me today but I can't get time off from work. My wife is going instead."