Sinusitis by itself usually doesn't cause a droopy eyelid unless there is significant swelling. If you have significant eyelid swelling then the sinusitis treatment may improve the ptosis (drooping eyelid) but I'd recommend a consultation with an oculo-facial plastic surgeon if you have a droopy eyelid that is not directly related to swelling that you get when the sinuses become infected (in other words, doesn't resolve once you use medication for the sinus condition).Best of luck!
It's important to perform sinus surgery to reduce chronic nasal polyposis and the repetitive infectious cycle inside the sinuses. Many cases of chronic sinusitis are caused from allergic nasal polyps located inside the nose. Allergies must also be under control with medications. The polyps are removed with endoscopic sinus surgery but they can come back unless allergies are under control. Some mild edema from the allergies may subside after sinus surgery, however it is doubtful that the droopy eyelid and swollen eyelids will go back to being normal. For more information about eyelid surgery and sinus surgery, please see the links below