I'm not familiar with the nose sores but I do get mouth sores like clockwork after every chemo. Biotene mouthwash is absolutely amazing for this. Rinse several times a day and they should be gone in a few days. There is also a prescription mouthwash called Neutrasal which your doctor can prescribe to you. My doctor also gave me a prescription for Famciclovir. It's an antiviral pill which I take for 5 days every chemo (starting on day of chemo). The first time I took it, it barely helped but it seems to be helping more and more each time (I'm assuming that's what's working) because my mouth sores are decreasing in severity. After this last chemo, I think I only used Biotene mouthwash a few times. Biotene also makes a toothpaste which you may want to try. (I personally didn't like it because it had zero mint flavor at all and was kind of weird but it's worth a shot).
Anyway, there are definitely things you can do to help so please ask your oncologist! Best of luck to you both! I hope John feels better soon.