Medicine Entrance Exam

According to the information you have given, Yes, you are eligible for admission in both the college's government and private for both the courses, B.Sc. In Nursing and BPT course. Because based on previous years' trends, a score of 250 or more on the 250 marks in the NEET exam is the safe score to get B.Sc. Nursing and BPT course. A list of government colleges for B.Sc. Nursing or BPT course:
1- Bombay Hospital College of Nursing for a B.Sc. Nursing.
2- Lokmanya Tilak Municipal Medical College and General Hospital, Kharghar, for BPT Course. A list of private colleges for B.Sc. Nursing or BPT course:
1- Sinhgad College of Nursing, Pune, for B.Sc. Nursing Course.
2- Ojas College of Physiotherapy for BPT course. I hope this will help you.

Yes, with 492 marks in NEET you have plenty of options to get into college for medicine courses. However, you are more likely to get courses like BDS BHM and B.A. MS than MBBS. You may get a government seat in a private college to pursue BDS as well as a government seat in a selected Ayurveda or Homoeopathy government college with your home state quota. You can get admission to the following colleges with your score:
For MBBS:
1. Agartala Government Medical College
2. Rural Medical College, Loni
For BDS:
3. The People's University of Bhopal
4. SRM Kattankulathur Dental College and Hospital
For BHM
5. Pratap Chandra Memorial Homoeopathic Hospital and College
You can also use Shiksha's NEET college predictor tool https://www.shiksha.com/medicine-and-health-sciences/neet-college-predictor to get an idea of all the colleges where you might be admitted. This tool uses previous year's closing rank data; hence, the results obtained are just indicative. The actual results may differ.

It is difficult to answer accurately in the absence of your category and home state data, but you may have a chance to get admission to government medical colleges (GMC) with 590 marks. According to previous year's cutoff data for GMCs, if you belong to the general category, you need to score more than 600 marks in NEET to get admission to most colleges. If you have a category-based exemption like OBC or SC, then you may get admission with a score above 550. Still, some medical colleges can provide admission to the open category by way of a stray vacancy round with a score less than 600. For instance, you may get admission to the Atal Bihar Vajpayee Government Medical College. Also, with category-based exceptions, you may easily get admission to the government medical college of your home state. For example, if you belong to Maharashtra, you may get admission to the Government Medical College in Nagpur.