I have bronchitis and have taken methypredisolone along with afrin for congestion. Can I take flonase or budesonide nasal spray for runny nose?

Yes. Nasal steroid takes several days to get optimal results . Afrin should not be used for more than 5 days else you may end up with even more nasal congestion (rebound). Methylprednisolone is not usually indicated for bronchitis. If chronic this may be asthma. Consider seeing an allergist.