Once I'm married, does the clock not stop on the 90 day count down?
As far as I know, it does not (and I'd be somewhat surprised to hear that it did).
If not, once it runs out will I be kicked out of Poland, even though I'm married?
About that I wouldn't like to say.
Basically you need to check now
where you local foreigners office is and what time they open on Monday. Then go there next Monday. Apart from anything else, you need to apply for a residency permit at least 30 days before your 90-day visa expires.