Hello,
since I've gone through tonsillitis quite recently myself, I would definitely say if that kind of infection spread to my sinuses - it would sound just as you described. But what strikes me as extremely odd - your doctors did take a culture to determine it was yeast infection in your throat - but did they do the same for your nose/ sinuses?
Thrush infection can spread to sinuses and if it had that much time to spread, while you were treated with antibiotics, it could easily be the cause for pressure and headaches. What I'd recommend you to is to ask your doctor to do a culture to determine what exactly is causing the sinusitis and if it's the thrush (or even bacteria) - it can be treated fairly easy. It's just important that you get the right diagnosis on this one.
Wish you all the best!