I am really sorry to hear that you are in such a difficult situation.
As your case is very urgent and complicated, I would highly recommend you to look for professional legal advice. I found this organisation, which has offices in various cities in Hungary. Maybe you can contact them https://menedek.hu/en/activities/social-work.
In the EU, the The Dublin III-regulation is determining the state which is responsible for an individual asylum procedure. As Hungary granted you a student visa, Hungary will unfortunately most probably also be responsible for processing your asylum application. In any case, as the refugee law in general is indeed complex and sometimes non-transparent, I hope you find the opportunity to discuss everything with a counselor or a lawyer.
Good luck with everything and please get back to us, if we can support you somehow.