The shortage is not due to an aging population, it's because nobody wants to go into this field.
And that is due to the pay not reflecting the extreme exploitation of the workers, in an environment that's not very conducive to a happy life. They all end up burnt out and have nothing to show for it.
They tried keeping the pay down by hiring Eastern European medical personnel, who would work below their qualifications (doctors as nurses for example), but apparently they don't want to work here anymore.
The problem has been going on for such a long time it is now systemic.
Seriously, "aging population"?
1347 was the first year of the plague.