You should seek competent legal advice from someone with experience handling asylum cases, which may include local immigrant legal-aid organizations.
Even with permanent residency, traveling back home or even using the passport of the country you are claiming protection from can put your status at risk:
If your travel abroad suggests that you no longer need the protection
of the U.S., your status as a refugee or asylee may be terminated. If
you return to the country where you experienced past persecution or
claim a fear of future persecution, you may be required, upon your
return to the U.S., to explain your travel to that country to avoid
losing your asylee or refugee status.
A person granted permanent residence based on a grant of asylum is
still subject to the possible consequences of returning to the country
of claimed persecution. An person's asylum status may be terminated
even if the individual has already become a lawful permanent resident.
In some limited circumstances, you may be able to return to the
country you fear if your stay is of a short duration and you can
demonstrate that your return to that particular country was due to
Here's a useful blog post by an immigration lawyer who specializes in asylum matters: You Can Go Home Again (Sort of): Visiting Your Home Country After a Grant of Asylum. He writes on the ways such a trip could jeopardize your immigration status in the US, both now and if you later wish to apply for US citizenship and suggests collecting evidence about the nature of the emergency and consulting an attorney before you travel.
This trip puts your ability to return to and live in the US at risk. That's too important to rely on advice from strangers on the internet. Please get professional advice.