As far as I can remember, you're not eligible for a J-1 Visa if you already hold a US CPL. The most you can have is a US PPL. An H Visa may be a possibility but generally the only people who succeed in getting one are already employed as a CFI by a flight school (usually with a J-1 Visa), have done a decent job, and are able to convince their boss to help them out. I don't want to kick you when you're down but: why didn't you research the Visa situation before you got your US CPL?