Hi Arnab,

Yes you can choose to apply for upgradation and wait for 2nd round counseling. There might be a minimum fees which they'll ask for. Pay the fees and sit in second counseling. There are more than one round because of the seats left after the 1st round of the counseling. Some students don't know about Mop-up round and stray round, which are the special round of the counseling to fill all the left seats. This is a link for schedule and all other important information about NEET counseling round 2, https://medicine.careers360.com/articles/neet-counselling. Always be updated with dates, don't miss out any date. 

All the best and do ask for any further queries.