Awww bless her....poor girl!
I would say definately an allergic reaction to something, it may be enviromental rather than dietary.
From what you've already said the only recent changes in her life have been the gym, I would remove all the fibrous things like the sisal and carpet for starters until you get to the bottom of it all....even that dandy little rope bridge should go for now!
Then maybe disinfect the whole gym area just as a precautionary measure to be on the safe side.
It might be as simple as sisal rope thats been contaminated with something whilst in storage thats causing it all, did she play excessively with anything in particular because it really looks as if she's been rubbing up against something?
And also you shouldn't rule out insect bites, especially with the weird weather we've all been getting lately...we've had pure quanties of beetles and flying ants swamping us out over here!
It is strange that she's the only one thats suffering, but I guess allergies don't affect humans all the same way so why should it be any different for felines. I can recommend something for her sores though, we've always used Sudocrem for things like that.....Just dab it on her sores very lightly whilst she's sleeping so no-one trys to lick it off before its absorbed, keep applying for about a week and hopefully she should heal up nicely.
It really helps with the healing time, and will stop it from irritating her as much after it starts to scab over!
Let us know how she gets on Paddy.