I've been told that if it's the car I'm bringing with me that I will be allowed to register it
No. You can't register it period. I know because I tried to do it myself with my RHD van from England. I have blogged about it here.
If you know someone who has registered a RHD vehicle in Poland in the last 3 years then get them to post on here how they did it because under the current rules it's not possible.