I recently need glasses as I can't see anything near - so need reading glasses.
Should I wear glasses when photographing or does the adjustment on the diopter adjustment take this into account?
So, am I taking blurry pictures that just look sharp to me?
It doesn't really matter whether you are wearing glasses or not assuming you have enough adjustment in the diopter. Adjust that, but don't look at what you can see through it, look at the viewfinder info (focus points, aperture setting etc) and make sure they are sharp.
If your camera has any form of live view (viewing image on LCD in real time) it may be a better option to use that for focusing.