Not "go to see a doctor" but just "see a doctor" or "go see" (where I live).
Either "go to" or "see" is fine where I live.
If don't feel better by tomorrow:
I'll go to the doctor.
I'll go see the doctor.
I'll see the doctor.
You're still sick? Did you see a doctor? Have you been to the doctor? have you seen a doctor? I thought you were going to the doctor?
Student or Learner