how will police that I came here for short time or forever
They will find out when you are stopped and asked to produce your insurance & license....which can't be just a state license as you probably already know. I think you'll need to take a Polish driving exam after 6 months as well. poland.usembassy.gov/poland/driving.html
I think the grace period though is less than 6 months, I think it's more like 6 weeks.
Best thing to do would be to get in touch with your embassy in Warsaw and they'll point you in the right direction.
There's a similar thread from a year years ago: https://polishforums.com/law/poland-import-car-15356/
There's also this:
Good luck, sounds like it's gonna be a headache.