Ask why the school did not give you the form. Technically, you are out of status because your H1 I-94 expired, and that may be the reason that the school did not give you the form for your change of status.
Two possible choices:
1. talk to your school (employer) whether they can extend your H1.
2. If choice 1 does not work, you may talk to your hu*****and's school to give you the form and go to Mexico (or China) to get the J2 visa to come back as that school previously suggested. I do not think you have any problem to get the visa if you can apply for it in one to two months. So, just talk to the school about that. You has been unlawful present, so the time is urgent to you.