As you have mentioned that you score 91 percentile and your rank is above 96k, there are very less chances of old and top NITs. Depending upon this year's seat allocation you may get new and low ranked NITs. One more thing to say, as you didn't mentioned your desired branch, so to be frank if you are looking for CSE or ECE it is again a big deal for you with this rank. So it's better to go through counseling procedures and see if there is any chances.
I would like to mention one more thing here you msy try for some state universities or some good colleges other than NITs for your B.Tech program.
All the best.