@A MyCOPDTeam Member Talk to the people from whom you got your oxygen equipment to see if they can help you set up a system to help you take in a water mist with your oxygen. That will keep the nasal passages moist and help prevent nosebleeds.
I can second the recomendation for Ayr nasal spray. It's simple saline but so effective! I keep one by my work desk and one in my kitchen. When the furnace really starts to dry out the air, this product is invaluable. I get it on-line but I think it could be available at a local drugstore, also. It seems to run under $5 a bottle, so worth it.
Ayr gel is also good to keep the nose hydrated. Increase your water intake as well.