Dear Prateek, last year score of 349 was enough to secure seat in GOVT medical college in West Bengal under STATE QUOTA for SC CATEGORY.
At 370 you stand a fair chance of getting seat in medical college.
Here's the list of Medical colleges whose cut off was less than your score.

• Bankura Sammilani Medical College, Bankura-356
  
• North Bengal Medical College, Sushrutanagar-367
  
• Midnapore Medical College, Midnapur-353
  
• College of Medicine and JNM Hospital, Kalyani-370
  
• College of Medicine and SagarDutta Hospital Kamarhati-369
  
• Murshidabad Medical College and Hospital, Murshidabad-351
  
• Maldah Medical College, Maldah-349
  
• ESI PGIMSR Joka Kolkota-357
  

Also since the exam was bit easy this year so the cut offs are expected to increase.
You can check the NEET college predictor to predict the colleges.
https://medicine.careers360.com/neet-college-predictor

All the best.
Feel free to ask for any query.