I doubt it Maisy. When mice start sneezing or have audible breathing, Baytril is usually the drug of choice as it`s an antibiotic (as said, prescription only) and the culprit is usually mycoplasma bacteria, or a secondary bacterial infection brought about by myco lowering the mouse`s immunity.
Using things like Vicks vapour and similar products can just iritate and there is nothing I personally know of (apart from fresh air) that will help a mouse to breathe better if it has these symptoms. I know where your coming from though regarding vets prices and if they would prescribe baytril on it`s own without the extra consultation charges, it would make it cheaper. I pay around £4.70p for a syringe of Baytril from my vet and even when I take one of the mice in, it`s normally not much more than this. But I know vets down south can be pricey.
If there is a home remedy for respiratory problems that is tried, tested and works, I think we could all save ourselves money! Some mice are just genetically prone to this and sadly, if they are not treated early, while signs are minor without showing abdominal breathing, constant sneezing and weight loss, they usually recover well.