...I totally understand your concerns. I teach third grade and have treated spots on my face twice in the last few years. Where masks can be a blessing for Efudex users wanting to hide the treated area, they can definitely irritate the skin. Any cloth rubbing my chest is intolerable when I have to treat that area.
I am not sure if it will help or not, but you might want to try a mask spacer. Amazon sells several different kinds. I have one and it works well to keep the cloth off my mouth and allows me to talk unhindered. Since you are treating the tip of your nose, you might be able to modify a spacer a little so that it keeps the cloth up and off your nose. The ones I have do touch the tip, but there are a few different ones out there, and you might be able to cut the middle section a bit to make it more comfortable.
I know face shields might not be acceptable at your school, but if they are an option, they could be a temporary answer for you.
I wonder if a mask that is shaped a little different might be more comfortable for you. There are many with vertical seams that might keep the bulk of the fabric from touching the tip of your nose. One of our teachers prefers to wear one of the disposable types that is more like a painter's mask. It's similar to the one in this link:
https://www.homedepot.com/p/SUPPLYAID-KN95-Protective-Face-Mask-CE-Certified-5-Pack-RRS-KN95-5PK/313331342
I have seen some made the same way and much cheaper at Wal-Mart or local dollar stores.
I will keep thinking about your dilemma and come back with more suggestions if I can think of some better solutions.
Here is an article that may help you as you are treating: https://skincancer.net/life-with-skin-cancer/tips-for-efudex-users/
I am wishing you all the best for an easy treatment and safe and productive school year! We are in this--all of this---together!
April, SkinCancer.net, Moderator