She needs to see ENT, asap - so per other posters, I'd make that your focus.
I've had grotty sinuses for years, prob since I was a child, although at first I did all the tonsils/grommets malarkey (well, it was the 80's...). Sinus prob weren't identified as the problem until I was 11/12? Once they were, I had a while with steroids (can't really remember which ones), but then was told that surgery was the next point of call. I had a relatively extensive surgery at 15 IIRC - 'all' my sinuses were blocked, the holes were too small. It was ok, cataclysmic bruising, but bearable pain wise! But surgical treatment has come on leaps and bounds since then, it's more refined now.
It bought me years of relief. But the surgery does not necessarily last forever. My sinuses are banjaxed again now, and I've even had a couple of bouts of peri-orbital cellulitis (as in your OP). Annoyed as sinus connection was not mentioned the 1st time... Anyway, I feel like shite again now, all day every day. 5 or 6 different types of headache, all at once; constant wooly head; poor sleep; searing pain if I lean forward, etc etc. As well as the non-painful things like: face sometimes looks freakishly puffy, I'm worried about bad breath again; blocked nose that makes my voice sound stupid... It's no way for me, a 35 yo to feel and it's absolutely not how she should be spending her teenage years, poor thing.
I need to go back to see drs, but putting it off as (with dc), not sure when I'd have 'time' for surgery. Well, I'm putting it off for lots of reasons, you know how it is! But these are critical years for her, and she will do so much better once she's back on par. I'd make a GP appt, and REALLY lay it on the line. And if no deal, I'd see the private fee as a great investment.
Best of luck.