Hey!

A marks of 370 will get you a rank between 155526-166885. You can check it here

It is quite difficult to accurately say about the chances of getting a seat since cut off varies every year based on various factors. But based on previous year cut off, you can have a chance of getting a seat in the following colleges since you have a domicile of Rajasthan -

Ananta Institute of Medical Sciences and Research, Rajasamand. Annual fees is Rs. 12,00,000

Geetanjali Medical College, Udaipur. Annual fees is  Rs. 17,00,000

Jaipur National University of Medical Sciences and Research, Jaipur. Annual fees Rs. 17,50,000

National Institute of Medical Science and Research, Jaipur. Annual fees is Rs. 18,50,000

You can know more about Rajasthan counselling and cut off here https://medicine.careers360.com/articles/neet-cutoff-rajasthan

Further, to get a list of colleges in which you have a chance of getting MBBS/BDS seat, you can use NEET College Predictor here