NEET

The fees for a Bachelor of Homeopathic Medicine and Surgery (BHMS) course in a private college can range from INR 1.5 Lacs to INR 3.5 lakh. Some private colleges with their BHMS fees are: 

College

Fees

KLE Academy of Higher Education and Research

INR 10.57 lakh

YBN University

INR 4.79 lakh

Sri Satya Sai University of Technology and Medical Sciences

INR 8.13 lakh

P. Savani University

INR 4.28 lakh

The BHMS course is an undergraduate course that lasts for 5.5 years, including a one-year internship after the final exam. The course covers all aspects of homeopathic medicine, which is based on improving the body's natural healing system. 

You stand a good chance of getting accepted into a government BAMS (Bachelor of Ayurvedic Medicine and Surgery) college with a NEET score of 433—especially if you fall into a restricted category. The number of candidates exam difficulty and seat availability are some of the elements that affect the BAMS NEET cutoff which changes every year. The qualifying percentile for SC/ST/OBC categories is approximately the 40th percentile (161-127 marks) but the general category's qualifying percentile usually falls between the 50th percentile (720-162 marks).
You might be in the competitive range for admission based on your score.

As there are 178 private and 41 Government Colleges in India offering BAMS course. According to N A RF report 2023 BHU Varanasi comes under 8 position and Dr.D.Y patil vidyapeeth Pune comes under 15th position. Some of the top government colleges for BAMS in India where BHU Varanasi, IPU New Delhi, CSJMU Kanpur, RGUHS and so-on. And they are collecting tuition fees which was literally between 1.2 to 3 Lacs at affordable cost.

Hello Vinod Ramesh Jagtap, on the score of 400 marks in NEET there are some BAMS college which you can get and they have annual fees less than Rs. 80,000 are as follows : 

1. Ayurvedic and Unani Tibbia College, Delhi: Total fees is INR10.73 K

2. Madan Mohan Malviya Government Ayurveda College, Udaipur: Total fees is INR 37.35 K

3. Government Ayurvedic College, Patna: Total fees is INR 40.5 K.

If you want to get admission in MBBS with this marks then it would be not great since you would have to pay a lot for it. But by my suggestion you should try for private university in ither fields for example BSC, BAMS, BHMS or etc. like that which would not be that much costly and can make a good in that field.

Also you can get addmission in many private universities so their is no chance to get dissapointed.

No, you can get B.Sc in AIIMS Rishikesh without NEET exam. (Hons.) Nursing cannot apply. B.Sc in AIIMS Admission to (Hons.) Nursing is through NEET UG examination. Candidates have to score good marks in NEET UG exam so that they can get admission in Nursing course in AIIMS institutes. This admission process takes place every year, and it is mandatory to clear the NEET exam.

With a rank of 3-4 Lacs in NEET and being an SC category student, you might be able to get admission into the following government colleges that are offering AYUSH courses (BAMS, BHMS, BUMS, or BNYS).
Government Ayurvedic College, Lucknow
National Institute of Ayurveda, Jaipur
State Ayurvedic Colleges in Rajasthan, Uttar Pradesh, and Madhya Pradesh
Government Homeopathic Medical College, Kolkata
The cutoff ranks differ from one year to another. Thus, it would be ideal to check the official portal for NEET counseling to acquire specific cutoff information about AYUSH courses.