It is likely down to a "link". The easiest way to check this is to go to the student record with the issue and click on the contact information cog. In the search criteria box enter the current Doctor's name for that student.
You will see a list pop up of all students under that Doctor. These students are all linked to that Doctor. Therefore when you change the Doctor here, it will automatically update all of the other students shown in that list.
To stop this, you will need to remove this student's Doctor's contact details by deleting it. Next, manually enter the new Doctor's details. This will break the link for that student.