From this page it looks like it actually runs on 12 volts.
http://www.westonshea...Catalogue-NEB91Q.html
There are two basic types of mains adaptor.
Transformers which are quite heavy and Switch Mode which are quite light.
Switch mode are really tolerant of voltage and don't care in the slightest about frequency. Often they will work from less then 100 volts to 250 volts and frequencies from DC (zero hertz) to 400 hertz.
The transformer types are fairly particular about voltage and the supplied adaptior is probably one of these.
Changing form 240 to 220 on the transformer type means it will only supply eleven volts instead of twelve.
However the increase in frequency from 50 to 60 Hertz will lower the magnetisation of the transformer and this will likely further reduce the output voltage.
You can be sure it won't damage the transformer or the nebuliser but it is probably going to run slower. It depends on the technology in the pump. It may even work normally.
However since you health depends on it I would be looking for a reliable replacement. I would suggest a switch mode type for maximum versatility.
Check out the markings on the transformer.
Aside from the 12 volts there are usually markings showing a number of Amps rated for the output.
This matters a lot.
There will often be mA for the input rating but this doesn't matter.
As switch mode adaptors are so light they are usually very powerful but you need to be sure it will do the rated current. You need one that will do at least as much Amps as the original.
You will also need to determine the output polarity (the orientation of plus and minus). Get this wrong and it can wreck the nebuliser.