Jhilkaydai,

You did not need to explain your Company's immigration that you had worked as an F1 without a work authorization. There's no relation to filing your H1b and working without work permit as an F1. There are many people who worked as an F1 (without permit) and how are H1B holders.

Also, if you go out of the country for visa stampping, they will not check whether or not you worked as an F1, unless they are real, real suspicious. Again, there are lots of folks who did work as a student, applied and got their H1B's, went for visa stamping (some went to Mexico, Canada, and even Nepal), and got the visa.

If your OPT expires in June, you have only 60 days grace period before which you should already have joined a college. Even if your application for the H1B gets aproved, you have to be in status until Oct 1st.

Good Luck