"Meddyg dw i."
Translation:I am a doctor.
So is there a reason that this kind of sentence breaks with the "dw i _" sentence structure we have learned prior to this?
Yes - see the course notes. When identifying ourselves or someone else particularly as 'an engineer', 'a teacher', 'someone called Dewi' and so on, we use an emphatic structure in the sentence, with the thing being emphasised being placed at the front:
Beth ydy'ch enw chi? - Dewi dw i. (What is your name? I'm Dewi.)
A beth ydy'ch gwaith, Dewi? - Peirianydd dw i. (And what is your work, Dewi? I'm an engineer.)
A beth ydy enw dy ffrind, Dewi? - Ceri ydy hi. Peirianydd ydy hi, hefyd (And what is your friend's name, Dewi? She's Ceri. She's an engineer, too)
At the top of this page, click on 'Topic: Welsh', then on 'Popular' anf then look for the sticky discussion 'course hints and tips'.
I presume this only refers to a doctor of medicine?
Somebody with a doctorate degree would be addressed formally as, say, y Doethur Gruffudd (= 'Doctor Gruffudd'). More usually, though, as Dr Gruffudd, as in English.
Why is "I am a physician" not correct ? Assuming term Meddyg does not include all kinds of doctors: PhD, ThD, DD, JD, LLD, EdD, &c.
'Physician' is fine. In some of the meddyg sentences it is accepted, but not in all of them by the look of it. We have no way of automatically adding it to every sentence, so it is best to stick with 'doctor' to be safe.
'Physician' is not a very widely used term in Britain.