The 3- and 10- year bar is triggered by unlawful presence, not unlawful status. Unlawful presence in your case would accumulate from the time that USCIS told you in writing that you were out of status and had to leave the country until USCIS (or the COurt) received your asylum application.
Andrew M. Bramante, Rosner Partners, 216-771-5588. Free telephone consultation. You should always consult with an experienced immigration attorney to make certain that the advice you received is appropriate for your particular immigration case.
Your status terminates when you stop attending college plus the grace period
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; 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.