Everything said so far is very true, but I suggest for future reference use F10 sc ( Its a bit expensive but really goes a long way! So on the long run its not so expensive) And you can use on your reptile cages for cleaning as well. Sunlight liqued will clean the cages but wont kill the germs in there. Now that said, it sounds like the new rodents did in fact carry something, that unfortunately I cannot help with, I suggest to quarantine them or to euthanize them for the sake of the healthy breeding colonies, but that is your decision to make.
It also sounds to me that there might me a mite problem in your cages, try using Carbadust in the cages to sort that problem out, just be careful which products you use, a lot of them is not healthy for rodents and some of them will kill the reptile you feed it to later on.
In my experience ( it can be symptoms of an underlying disease) sneezing can be that they are allergic to the shavings that you use or that they are to fine. Remember, shavings that is not sterile may have all sorts of chemicals in there as well as mites and fleas.
But for future reference, buy your breeder mice from a reputable breeder or a reputable pet shop that allows you to come and see their mice in captivity, it will save you a lot of money and peace of mind. I for instance like to keep track on my genetic lines.
And always remember this, this can safe your child and your animals life. PREVENTION IS BETTER THAT CURE. Keep a healthy environment and make sure the breeders you introduce are healthy.
This brings me to the age of your rodents, breeding them over the age of one year is to old. I replace my breeders every winter, the average age of menopause in a rat is between 15 and 18 months, its sort of like your grandmother having babies. I suggest replacing them with younger mice / rats. I prefer keeping some of my own mice to restock my colonies, but introduce new males or males from another litter. Make sure to use the litter of females that breed easily and have nice, healthy and big litters , in most cases that gene will carry over to the young.
As for the temperatures for small rodents, they prefer 22 -30 Degrees Celsius ( I think 21 the lowest), that the reason why I suggest a well ventilated room with fans if the temperatures gets to hot.
This wasn't a nice experience but a good learning curve.
Hope this helps with your future breeding!
Crazy, not stupid...........