and I think the personal allowance rather than being a fixed figure is calculated at 20%.
No, not true. The personal allowance is a mere 3,091zl a year - along with some allowances if you're married, have children, etc.
I have been told that if I want the personal allowance then I have to have residency, whether that means a NIP number or Pesel number I don't know.
Otherwise I will get the money back in Feb.
This is lies - for a start, the tax office won't return any money until after the deadline for submitting the personal tax return (deadline - usually end of April, give or take a couple of days).
Go here and see what comes out - then compare it to your own situation. The personal allowance will only come into play at the end of the year - as "income tax" is actually just an advance on your final tax bill rather than being an actual tax payment.
It seems to me that you've been told a load of rubbish by someone - you won't get a 23% tax burden in Poland - it'll either be 9.5%, 18%, 38% or 52%.
Do you know if you have "umowa o prace", "umowa zlecenia" or "umowa o dzielo"?