Talk with your O2 provider. They have a number of ways they can add humidity to your O2 delivery system. Things like Ayr Gel can also be used to keep the inside of your nose hydrated.

I use Flonase and Saline solution for the past 8 years. Works for me. I also use a humidifier in my bedroom at night.

Hi Christine. I thought this concern was covered by the Team not too long ago.
Here's the skinny on why the nasal passages swell ( as in congestion) when they dry out from Oxygen use.
I know you said your nose was runny. You have to read the article in-between the lines. Ask your equipment supplier or the Doc if more help is need to keep you comfortable.
Stay safe and be Well.
https://www.verywellhealth.com/how-to-prevent-n...

She's talking of stuffy nose, not dry nose. I'd also like to know why I have such a stuffed nose and have to blow for ages when I wake up and throughout the day. Decongestants, I know, can initially clear stuffed nose, but over time make the problem worse. Saline is all I've found, and steam. My mother swore by a running tap of hot water with your face over it and a towel over it all to steam clear you.

Are you using an attached humidifier? My provider did not supply it until I asked for one.