Can you tell me how long it should take antibiotics to get rid of a chronic sinus infection?

Varies: Sinus infections can be persistent. I would recommend you have a culture and sensitivity done so the correct antibiotics can be used. Depending on what bacteria are involved, a single or multiple antibiotics may be needed. 10 days to perhaps a month is the range.

See an ENT: Regardless, whether it's acute or chronic, sinusitis is painful and wearying. For chronic sinusitis, antibiotics and nasal corticosteroids and nasal irrigation are the main treatments. If refractory, surgery to be considered. Proper diagnosis is the key to successful treatment. See an ENT for evaluation, rhinoscopy, imaging and treatment.