Hello,
Yes no domicile requirement is there for private and deemed medical institutions.
you can easily apply to private and deemed universities of other states than your domiciles.so you can easily apply for punjab state counselling despite having a haryana domicile.
You can use careers360 college predictor to know the colleges you can get at your NEET score:- https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer