the fact that you had little response to medrol makes me think less of an allergic cause, although its still possible. since you have acid reflux symptoms this is a definite possibility. this is probably the second most common cause of undiagnosed chronic cough. you can trial prilosec otc if you have no allergies and provided you are on no other meds that may interact.
if no response in 10 days or so i would see an ent. they can rule out nasal/sinus causes and are also pretty keen at determing a GERD cause.