You might want to take some moistening supplements. I use marshmallow and mullein. Also large does of B5 are an enormous help. These are also anti-inflammatories. I rely on these supplements since I quit inhaled steroids because of serious side effects. You have to take 500 mg of B5 daily. For the other two I use the liquid according to instructions.
Oxygen tends to dry out nasal passagaes. The bloody phlegm is from the dryness and small broken blood vessles that result. Kind of like what happens in the winter when it is really dry and cold for a while. Your nose dries out and starts mild bleeding.