Medicine

Well, both are good at their level. If you are capable to pay the fee of MBBS then you should go for that. Otherwise, Physiotherapy is good option as well. But if your family is strong financially then go for MBBS. All the best.

Please refer the link for eligibility: https://www.shiksha.com/medicine-health-sciences/course/mbbs-sgt-university-gurgaon-196251.
If you meet the criteria and qualify NEET, then you can get admission.

For requirements to pursue MBA in hospital and healthcare management, check out the links below:
https://www.shiksha.com/mba/course/mba-in-healthcare-and-hospital-management-institute-of-clinical-research-india-Delhi-nehru-place-244623
https://www.shiksha.com/mba/course/mba-in-hospital-and-healthcare-management-Jaipur-national-university-251804

The colleges do not have an online admission process. Kindly refer to the link below:
http://www.kcps.ac.in/admissions.aspx

Getting any private college with these marks is not possible this year for general category as the minimum cut-off for getting any private college is around 450. You can try for management quota seats.

I am listing some top colleges on the basis of your general rank:
JSS Academy of Technical Education
JMS Group of Institutions
Rajkiya Engineering College
Purvanchal Institute of Architecture & Design
Galgotia's College of Engineering & Technology
Ideal School of Architecture
Sri Ram Group of Colleges.

Yes, you can get admission in KJ Somaiya medical college for MBBS with 377 marks in NEET.

You need to score more to get admission in Lady Hardinge College.

You should just go with MBBS from a local private college. MBBS had good career opportunities than BDS.