Oh my goodness, that’s got to be one of the worst styloids I’ve ever seen 
No wonder you’re feeling bad! The right side is obviously longer & thicker, the left side does look pretty long & angled too… I would imagine you’ll feel better for having it removed, I think reading the report as it mentions the styloid is in contact with the external carotid artery, this would be a concern for me, as it could potentially partially block the artery with different head positions, which can cause fainting, and if it was really blocking the artery then potentially a stroke. It also mentions at the end of the report it’s also in contact with the right Internal carotid artery, along with the pain you’re experiencing if left this might cause more issues for you. Having the deviated septum operated on in my opinion would be less of a priority, being intubated for surgery and having your head moved about during the procedure could also be a cause for concern given how long and angled your styloids are.
I would discuss your concerns about being in pain with Mr Hughes before surgery; you should be given pain relief having surgery here in the UK, apparently having a tonsillectomy as an adult is really painful, hopefully ES surgery won’t be as painful. You can use the search function to look up discussions about surgery with Mr Hughes, each doctor’s approach is slightly different so recovery will vary…
There’s a section in the Newbies Guide about surgery, there’s some ideas of what to expect & get ready beforehand, here’s a link:
ES Information- Treatment: Surgery - Welcome / Newbies Guide to Eagle Syndrome - Living with Eagle
It is worth being prepared for your other side to possibly feel more painful after surgery, it sometimes does that, so it might be at some point you’ll need surgery for that too…
Also, I don’t know whether you’ve tried much for you nose, my husband has a deviated septum & sinus problems, he struggled to sleep, but tried this product which has really helped him:
Airmax Nasal Dilator - Anti snoring Devices - Nose Dilator, Sleep aid and Snore Stopper - Breathe Right Through The Nose - Snoring aids for Men and Women - with Free Storage Box - 1 Pack - Small Blue : Amazon.co.uk: Health & Personal Care