Well, a possible solution (which I noticed OhLordly also suggested earlier), would be:
Table: patients
patient_id
patient_name
//other patient info
Table visits
visit_id
patient_id
visit_date
complaint
diagnosis
treatment
next_appt
Now, most probably the patient himself will not search for this info.
Rather the receptionist or medical staff may need this info.
As such, the staff member will first obtain the patient's name.
You probably would not use patient_name, but rather have different columns for name and surname.
From that, he can get the patient_id of that patient from the patients table.
With the patient_id, he can use another form to search for the patient's visits in the visits table.
patients.patient_id is the primary key of the patients table.
visits.patient_id on the other hand is a foreign key of the visits table.