It all depends on what is causing the sinus infection or bronchitis. Neither will help if the infection is caused by a virus or fungus, and rifampin is not a drug of choice for a bacterial sinus or bronchial infection. It is mostly used for tuberculosis.
Any infection should be cultured to determine what organism is causing it. Bacteria are then subjected to a sensitivity test that tells the prescriber what antibiotics will kill the bacteria and which ones it is resistant to. Viral and fungal infections do not respond to antibiotics at all. There are a few antiviral medications that are used for viruses and some anti-fungals for fungal infections.
Sulfa drugs are those with the sulfonamide moiety in them and include such things as sulfamethoxazole usually in combination with trimethoprim (Bactrim, Septrin, Septra). These drugs are used for urinary tract infections, for respiratory infections, and for skin infections like staph. They are also used for MRSA (methicillin-resistant Staphylococcus aureus) which has become resistant to many antibiotics like methicillin, penicillin, and amoxicillin.