Hello,
No there is no increase in fees for round 1 and for the subsequent rounds at private mbbs college. the subsequent rounds are jsut held for the seats that are empty from the previous round.(a drop in score cutoff is seen usually)

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