Asylum will now be a subject at any interaction you will have with the American government.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
You can travel with a valid H1B visa, but if you had a legitimate fear of persecution you might not want to.
Andres Mejer 9 Memorial Parkway, suite B Long branch, NJ 07740 220 Third Street Lakewood, NJ 08701 732-962-1805 www.AndresMejerLaw.com