M.Sc Chemistry

As a chemist, I would recommend the M.Sc in Chemistry because it is more general. Biochemistry is specialised which might narrow down your future career possibilities.

1. University Institute Of Chemical Engineering And Technology
2. Government Medical College And Hospital

If you go with Industrial chemistry you have only few options, if you go with chemistry you will be having a lot of options.

I think M.Sc. will be a better option for you if you do it from a good college or university.
You can Pursue M.Sc. from IIT's or IISC. For Taking Admission in IIT's you have to appear in IIT JAM Entrance Exam for M.Sc.
Click here to prepare for IIT JAM Entrance test - https://scoop.eduncle.com/iit-jam-exam-syllabus
I hope it will help you.
Best of Luck.