Moving in Europe (Dublin Regulation):
Starting international protection procedures on Polish territory means that you are subject to Dublin Regulation: first country where you ask for international protection (in this case Poland) is responsible for your procedure. It means, that during procedure that can take from couple months up to couple years, you will be not allowed to leave Poland.
If you will leave and ask for international protection in different country, you will be most likely send back to Poland.
Only after getting international protection you will be allowed to travel Europe for 3 months without visa. But only in Poland you will have the right to settle permanently, work without permit and have social support.