What you and your cofounder is doing now (working part time on your web-app) is probably already illegal while on your H1B, even if you're not getting paid. If

What you and your cofounder is doing now (working part time on your web-app) is probably already illegal while on your H1B, even if you're not getting paid. If you have incorporated in some form or another it's definitely illegal. Be very, very careful. Your best (only?) option to have your own company sponsor you is an O1 visa.