Hi Kushgra,
I wonder why you want to shift from your present career, as it is still a good one though with numerous hospitals, health institutes and wellness centers coming up.
But still, now that you have asked, there are some factors that you must look into before you take up a Career as a Graphic Designer:
1. Passion for the career; however as you have already mentioned you have passion for the career then it will not be an issue at all.
2. Age: Though it would not have been a problem if you made a career shift in your domain, but coming into graphics designing is completely new domain. Still I will not discourage you if you have it in you. Still as the saying goes "There is no Age for Learning"
3. Openings in a Graphics Design College: you must find good trustworthy graphics design colleges that will offer you the best course and learning aids and infrastructure that will not only well teach you Graphics Design but also will provide the initial placement support or at least an internship opportunity so that you can set foot in the industry and gain confidence.
Now to your last question will starting a career in Graphic Design in India the correct decision?
The answer is if you have the passion, grow the skills, learn the techniques, get well-versed with the technology, and come up with problem-solving situations, this will be a decision you will never regret.
Rather the patients at your hospital will miss a good nurse....
Hope and wish you all the luck in your journey into Graphic Designing and wish you all the success.