Augmentin hasn't worked on my chronic sinus infections either, and I've fought them for 3 years - since a wreck that broke my nose and displaced my septum. Bactrim stops it for a couple of weeks, then it comes back.
Did your ENT send out a culture? That should find out if your bug is susceptible to the treatment. It doesn't work if the lab doesn't test for unusual bugs though. I've had Moraxella a couple of times - got it from grandkids. Doxycycline for 3 weeks cleared that up when grandkids who had it were treated with something other than amoxicillin also. It can take a few weeks to culture some bugs. When I've been found quickly to have more or less normal flora, treatment (usually Augmentin) hasn't worked.
The culture could also find a fungus.
If your bug is treatable with Augmentin it can take 3 weeks, maybe more. Sinuses don't have a lot of blood flow, so it's hard to get treatment to them.
I get some relief from rinsing sinuses several times a day, especially when I use a steroid in the rinse. I've tried things for a year to get one that is useful and somewhat affordable. The sprays haven't worked at all for me. I prefer sinus wash with Neil Med bottle. It delivers more to my somewhat blocked sinuses (even after sinus surgery). The small bottle that came with the rinse is useless and netti pot has no pressure, which I need.