I have a USA driving license that expires in 3 weeks and am trying to figure out how to replace it here
You will have to pass a test to get Polish license which will first be issued for as long as your US license is valid meaning for 3 weeks as you have mentioned but then you will have to get a medical test to prolong your Polish license.You can go to any General doctor for the medical exam,I got mine that way they issued license with no expiry date but now I heard they issue for 4/5 years and you have to renew it.Yes taking a Translator always helps:) and in my case was mandatory.
I would suggest you renew your driver license in US first as you don't have much time left or go to AAA site and apply for a IDP(International driving Permit) which is good for one year for you to drive.I don't know if Polish authorities change IDP to a Polish license and they will keep your US license when they issue you Polish license but you can always get a duplicate one in US
Also you will need a sworn translation for your license(front and back) and you have to be careful as the categories are different in Poland then in the states.
I changed my license in 2003 so rules might have changed now.