The picture below shows the footprint I used in my layout. But when I printed my layout on paper, the drill size doesn’t seem to be big enough to fit my actual component.
Well that footprint is probably not made for your component then
One footprint can not be made to fit all possible components that could be used there.
That’s why most of us have our own tested personal libraries that fit our needs.
By the way is your display the same as specified in the footprint? (Same manufacturer, same type: Kingbright CA56-12 or CC56-12)
These are the parts for which the footprint is specified. It is not guarantied to fit any other part!