If I may, particularly as a doctor yourself, you should call the eye doctor "ophthalmologist", as you surely know if you use "part of the body + doctor" there might be issues should you report a visit by a "proctologist" ...
Why replace a good, short and clear word with a bad and long word that adds no information, but fewer people will understand? [Edit: I think I'm wrong about the adding no information, depending on country there might be other types of eye doctors than ophthalmologists]
The way I typically like to use terms of art in writing is to write the term out first, and then a parenthetical with a definition. For example here you went to see an ophthalmologist (eye doctor). It's also good for acronyms and initialisms.
