Yes you can appeal to the Board of Immigration Appeals within 30 days. The asylum process provides for a hearing in front of an immigration judge.
Finally, on appeal if the Board affirms the immigration judge's decision, you would have 30 days within which to appeal that decision to a federal appeals court.
You need to get an attorney too help you fix this. The Asylum clock is a major problem. Check with a lawyer in your locale to discuss more of the details.
Good luck to you.
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I would strongly suggest that you consult with an immigration attorney before you do anything. The denial rate on asylum applications is very high, depending upon the country in question, the specific facts of the case, and the Immigration Judge that you get assigned.
Syracuse University did a study of all the IJs in the country and ranked them, by how often the granted asylum. The range was between on judge in Miami that denied 96.7% of all the cases he ruled on to one judge in New York that only denied 9.8% of all asylum case.
Once you receive a denial, then you become subject to a final order of deportation, pending appeals. However, with a final order of deportation, your b/f will be ineligible to adjust his status, even if you marry and have a visa available for him.