Welcome --
I don't know about Pseudomonas, andn as mojo says, that's something your doc will have to speak to, and I would put in a call and tell the person on the phone what's going on so they can advise you sooner rather than later.
The nice dark, moist sinuses are definitely areas where fungal or bacterial infections can hide and multiply, and the sooner you get it sorted out the better.
I had a similar situation but in different circumstances (no CPAP, but a fungal infection from some yeast-based priobiotics I was taking) and it really needs to be properly diagnosed and treated with the meds that are effective against whatever the bug is (whether fungal or bacterial or whatever) and also preventive measures taken to ensure you are not accidentally re-infecting yourself with a possibly dirty CPAP system -- so I think you are on the right track with your questions.
Do call the doc's office as soon as you can -- best wishes -- let us know what you find out, okay?
Sorry, that is something I don't have experience with and not sure if it ties into Lyme disease.