If he does have a minor respiratory infection, you can treat him with Tetracycline. This is an easy, low cost, and safe way to treat RI without having to go to the Vet. However, it won't cure advanced stage RI.
You can find Tetracycline powder in the fish section of any big box pet store.
One box contains about 10 packets of 500mg of powder and cost about $12.

One packet mixed with water can be used in a 16 qt water bottle. You would need to refill and change it daily.
It takes about ~2-3 weeks for the rat to fully recover from RI.