I had the dry nose problem for several months when I first went on oxygen 24/7 a little over a year ago. It was beyond horrible. I was frantic and no one seemed able to help me, just looked at me like I was crazy. My nose was constantly bleeding, then scabs and so full of yuk I couldn't breathe through my nose!!! Now what?
I finally got some good info from a nurse. She suggested trying Ayr Saline Nasal Gel. I got some and it helped a bit, but didn't solve the problem entirely. She then suggested I try PONARIS, Nasal Emollient and thank God, it has helped tremendously. Neither one is expensive and it's such a relief. I highly recommend the Ponaris. I do switch off on occasion and I use a humidifier in my bedroom while sleeping. I've also had to use Flonase and recently a new one that doesn't dry me out as bad, it's by Rx only, Azelastine nasal spray. The Flonase and Azelastine are more for allergies that have always bothered me, add that on top of a nose that is crusted with blood and a mess and it's a real problem. The cold dry air of winter sure doesn't help the situation. Definitely DO NOT use petroleum based products in your nose. Oh, and I use Ocean saline spray as well - twice a day to rinse nose out, then put the Ponaris inside with a Q-tip instead of the dropper they have as I found it too greasy. Stuff worked like a charm to heal my nose. Best wishes. I know how miserable this can be, and found out it takes a lot of time to get all the info you need. Didn't seem that any one doctor could give me all the information I needed.

If your on an in-home oxygen machine, your provider can get you a water bottle that attaches to your oxygen tube to keep your nose moist. Your oxygen machine should have a place for the bottle. You have to use distilled water in it. I had the same problem at first, then I called my medical supplier and asked what to do and they sent me out the water bottle.

AYR nasal spray helps

I use a Oxygen Humidifier Bubbler Bottle - Humidity for Oxygen Therapy Drive Medical company at night on my large oxygen concentrator and it does help. if not they have it on @Amazon for about $8. I use boiled water that we keep it in the refrigerator per the doctor. the tip in the bottle gets clogged after a while and I sock it in vinegar and that clears it

Try Ayr gel. It's not petroleum based.