Is it necessary for me to apply for international protection immediately if I want to stay inPoland?

No, it isn’t. You are granted temporary protection if you have arrived in Poland since
February 24, 2022 provided that: – you are a citizen of Ukraine – a person with
refugee status/international protection in Ukraine – a member of your immediate
family, the above-mentioned persons. Temporary protection may also be granted to
individuals who hold a permanent residence permit in Ukraine and cannot safely
return to their country. Considering whether you entered Poland legally and whether
you are a citizen of Ukraine or a third country, your rights and the period of your legal
stay will be determined differently – according to the Act on Foreigners Protection in
the Republic of Poland or the Act on Assistance to Ukrainian Citizens in Connection
with Armed Conflict in the Territory of the Republic of Poland.

You can find more information here.

If you are a third-country national and do not belong to the above category of
persons, find out what options you have for legalising your
stay here