Frequently Asked Questions - H-2 Visa

J-2 to TN

You can switch back to TN. To correct slightly, you do not automatically get switched to an H-4 (not H-2).

H-2B Visa

Assuming you have no home residency requirement, you can start the H-2B process even while you are here in USA.

Marriage to US Citizen

I see no reason to wait.

Are H-1 holders being turned back at the airport?

If this is all what happened, then the govt. has acted illegally. There is no question in my mind about it.