B.Sc

PGT stands for Post graduate Teacher. And eligibility criteria for a PGT is a Masters degree (in any discipline) from a recognised university, B.Ed or equivalent degree from a recognised university. So, as per your question, you have completed your Masters in Biotechnology, but for a teaching post like PGT you need to complete your B.Ed as well.

Some of the colleges offering this course are:
Lovely Professional University, Jalandhar
Sharda University, Greater Noida
Manipal University, Manipal
Swami Vivekananda University, Sagar.

B.Sc. Nutrition would be the better choice based on your future plans. But I would suggest you to find a Masters programme.

so you might be covering with all the marks that is actually required for general category else it will not be possible.

The top institute for B.Sc. Chemistry in India is Jaipur National University. Duration: 3 Years
Eligibility: 10+2 minimum 45% marks at 10+2 level or equivalent with English as compulsory Subject
Selection Procedure: Merit and PI
All the technical and professional programmes are approved by various regulatory bodies - AICTE, NCTE, BCI, INC, PCI, MCI. The University is the First Private University of Rajasthan to be accredited by the National Assessment and Accreditation Council (NAAC), based on a very comprehensive evaluation and accreditation only after 7 years of its establishment. Visit: https://www.jnujaipur.ac.in/.

M. B.A. In hospital management is bound to the only hospital sector. But as per the current scenario, the hospital sector is growing. Also, more advantage is you are belonging form nursing background. You know whats the problem and the solutions regarding the hospital management system. An MBA in HR is not bound to the specific sector.

Which college or university?

Use this link:
https://www.shiksha.com/college-predictor