Have you tried a Netti Pot, nasal saline irrigation?

I feel your pain. While in remission with my CLL sinus infections were a constant issue for me. We used one antibiotic after another and nothing seemed to work. Perhaps a referral to an ENT might help.

Sounds like chronic sinusitis.
Netipot may help.

Frustrating for sure. Do you have allergies of any kind (seasonal, dust, animals, etc)? Allergies to whatever can often lead to recurrent sinus infections because one is not getting to the root of the problem. If the antibiotics aren't working, then they are only masking the problem and also depleting your immune system and killing the good bacteria. Worth asking your doctor if you can get a referral for a allergist/immunologist doctor in your area.