Hi Vee. Have just read your post and so sorry to hear you're struggling. Please don't give up as your health is likely to go downhill. CPAP is hard for most people, and even harder for others. Check out this video on Claustrophobia, and there's lots of other videos in the series http://youtu.be/CtmCJxMvsuM
There is a products too that can help with dry mouth, which can also be used whilst sleeping. I've not tried it myself, but here's the linke http://www.orahealth.com/products/xmdm/
Do you use a humidifier? If not, then that can help too and the hospital should supply you with one.
I don't have rhinitis, but have had 2 nose operations due to a deviated septum. I use the Breatherite Nasal Strips (which you can get on this British Snoring site. I use them all the time and have come off Nasonex since I've been using them.
The hospital are trying to persuade you to use a full face mask due to your nasal issues as you probably mouth-breathe due to this, but there are lots of masks on the market that feel less claustrophobic. My 2 favourites are the FitLife by Respironics, which looks a cumbersome mask, but in actual fact doesn't feel that way when it's on. There's a clear line of sight too. The other favourite of mine is the Innomed Hybrid, which has nasal cushions plus a mouth cushion. Try Googling them both to see what you think.
Good luck and hope this has been of some help!