I have been in the same situation last september. My OPT expred on July 11th and H1 was valid only from OCT 1ST. Since your OPT expires on May and H1 starts at around Oct 1st. You have a grace period of 60 days (not 2 months). After the 60th day, either you have to start school or leave the country and you can re-enter the country after OCT 1ST. During this 60 days, you CANNOT work, unless you can have them pay you under the table. I was here for 60 days after my OPT expired and then I just went back to nepal and came back on OCT 6TH. Hopefully this helps!!!