In general, first to qualify in NEET, a General Category candidate has to score 50% of the top NEET score. It is 40% for SC, ST, OBC. For example, if the top NEET scorer has scored 500, General Category candidates should score atleast 250 and SC,ST,OBC should score around 200 to qualify. Now not every qualified candidate can get a medical seat. It depends on cut offs. Now cut offs change every year and are dependant on various factors like no.of seats available, no.of candidates appearing for the exam, difficulty of the exam and top NEET score. Every State except Jammu and Kashmir has All India Quota and State Quota and there is different cut off for each quota. Now every State has various cut offs for every college and Category. Tamilnadu is one of the States with highest cut off. But States like Assam do not have that high cut off. So it totally depends on what State you want to apply and if you want to apply under All India Quota or State Quota. State Quota has higher cut off marks. For Tamilnadu, it should be atleast 625. But for Himachal Pradesh it is around 300. And you cannot be eligible for State Quota of every State which means you should also try for All India Quota. But without having an idea of which State you want to apply for, it is difficult to guess your chances. For example, with the cut offs that Tamilnadu has, one can easily get a seat in a Govt. Medical college in West Bengal.

With 361 marks,you may get into a deemed university/college. You need to fill your choices carefully and keep a close watch over the whole counseling process as to when n all the counseling rounds r happening,their reporting time and all.And also you got to check the respective sites of the college for information regarding the manual rounds.Its not gonna be an easy process .You can try for the colleges in South India because they might be charging a high fee but they provide quality education and have proper infrastructure (such as Shree Ramchandra 22lakh +,A few colleges in Kerala, Karnataka and a few in Pondicherry).For more information check the respective sites and last year statistics and you might be able to get an idea.

Collage allotment will depend upon the merit list but you can visit this site for a clue

https://medicine.careers360.com/articles/neet-college-predictor