It seems you didnt apply for change of status. Infact if you file H1B on April with opt ending on May, you cannt file change of status at that time. Did you apply for change of status after you got I20? If not you are still in F1. In such case you should leave the country and enter with H1B by getting H1 visa stamp. This what I see from your explanation. To make matter clear, talk with your attroney who filed your H1B. He/She knows better.