I switched some time ago to using cloth hankies for everyday use. I use upcycled flannel from old sheets and make them on the smaller size so that they fit in my small pockets, and so I can toss them in the wash regularly.
I admit, I haven't caught the Martian Death Flu (substitute whatever the current concern is). If I did, I would be willing to use tissues, put them in a paper bag, and burn them in our wood-stove. So realize that I am asking the question regarding the everyday sniffles, often from pollen outbreaks, where it seems to me that the comfort of flannel is so much nicer on my nose, the flannel doesn't fall apart from repeatedly being jammed in my pants pocket along with keys and pocket knife, and that doesn't fall apart in the wash when I forget to check that one... last... pocket...
If you do want to sew your own, this thread is for you:
https://permies.com/t/177617/Making-Hankies
It has lots of great info and may try to influence your feelings on the subject.