My question is, what will change about my status in Poland?
Nothing. You'll still have to apply for residence permits and so on - except you won't need a work permit.
In a place like Bolivia for example, you can travel there without a visa as Polish citizen but not as a US citizen. So in order for me to meet the standards of a Polish citizen would that mean I need to have a Polish passport?
Yep. Marriage will only give you the right of working and residence in the EU, nothing else.