This past shabbat our young son suddenly developed a frightening kind of breathing and cough which is supposed to be treated with a nebulizer. We assumed it was okay to turn it on (and as there was no difference in quality of care, we turned it on with a shinui). However, after being left on for a long time, it was producing a smell of burning plastic, and I was worried that it would break and we would not be able to use it for his next treatment (which would still be on Shabbat.) Therefore my husband turned off the nebulizer with a shinui, and I did not stop him. In the end we did not need to give him another nebulizer treatment, because a more effective medicine was located later on. Were we wrong? How can we do teshuva? Thank you. We are Sephardic.
It was allowed, even if this was a non life threatening situation. Turning on a nebulizer with a shinui is allowed if the child has the halacha definition of a “sick person”. From your description it seems that he was in this category, especially if he is under the age of 9. Since you thought you would need the nebulizer again, and you thought that it would break if you left it on, you were allowed to turn it off with a shinui. (In addition, if the nebulizer could cause a fire, it is usually a case of pikuach nefesh (danger to life) and you would be allowed to turn it off).
There is an important point that has to be made. Turning on a switch with the left hand is not much of a shinui because a switch is easily switched on with the left hand. In order for it to be considered a shinui you would have to turn the switch on/off with your elbow for example.
May your son have a speedy recovery and a refua shelaima
Turning the nebulizer on/off- Shulchan Aruch 328:17, Mishna Berura 328:57 (in this case where the melacha is mi’derabbanan (shinui) and it is מקום חולי, we can consider electricity to also be mi’derabbanan, and therefore it is a case of melacha de’rabbanan bi’shinui which is permitted for a sick person).
Regarding left hand not being considered a shinui- Mishna Berura 340:22 (towards the end) in the name of the Chayai Adam. Cf Shevet Halevi 7:64