Is there any in universe reason that she couldn't have been training as an MD whilst still nursing ?
Err, because she was busy serving on a starship way out on the frontier at the time? I'm not sure earning an MD is something you could do as a correspondence course.
Besides, as I just pointed out in another thread, Ogawa's most recent appearance to date as a nurse on Titan
) is set just two months before her appearance as a doctor on Challenger
in IFM, in which it's stated that she joined Challenger
's crew "some time ago." Given the lengthy travel time from Titan
's survey area back to civilization, that's quite difficult to reconcile.