Staying in US after H1B expiry and new visa in process

My current H1B ends on June 30, 2014 and I-94 expires on July 10, 2014.

My H1B application is selected in the lottery and is being processed.

 

Since the new H1B does not start until October 1st, do I still have to leave the country? Am I allowed to stay because I have a pending H1B processing?\

 

If not is there any other visa that I can apply for? like B1?

 

Please advise!