I know exactly what you are going through. I have a sinus infestation of threadworms (strongyloides), and when they started to die, my nose and sinuses dried up too. Their irritation was what was causing me so much stuffiness. I can breathe better now, but I was still concerned about the dryness, so I searched for something to put into my nose that would not hurt me, and I found coconut oil.
I have posted several times here about threadworms and what they look like when they come out. Some are quite long (they reach full size in 5 days) and have blood in them, and some just curl up and come out of my nose as little white balls. When I take a pin and stretch them out, you can see the worm.
I am using coconut oil in my nose, and even snorting some up into my sinuses. I swab my nose with it several times a day, and pull about 5-10 threadworms out. If I wait a few days, they get very bad. They seem to multiply very rapidly, and I read they are very hard to get rid of.
When I was doing my first Humaworm treatment, it controlled them, but once I stopped, they came back. The thing is, it only kills the eggs in your digestive system, so you have to constantly kill the adults. I'm going to be doing my second cleanse in a few weeks, and I'm convinced that what I'm doing now in conjunction with the next round will just about do away with them.
Humaworm also makes a cream that people have said they put into their noses and had worms come out. I used the coconut oil because I couldn't afford the cream, but if you can afford it, I recommend it.