thank you for sharing your question with the Wefugees Community!
Unfortunately, I am not an expert in this field since I am located in Germany and not in the Czech Republic. But i did a little research and I found this leaflet by UNHCR (United Nation High Commissioner for Refugees) about the asylum procedure in the Czech Republic. It contains all the basic information about the procedure and also some useful contacts to refugee aid organizations:
I am sorry if I can´t help you any further. But maybe someone else from the Wefugees Community has more knowledge about the system in the Czech Republic!
All the best