Hi Shreya,
I definitely recommend doing a Master’s program before entering a design career. It will be a great training where you can go in-depth and explore the kind of design you want to pursue. Eindhoven University in the Netherlands will be a good program for you - you get individual guidance, work in teams and can work on various kinds of design activities and always involved in the groups doing presentations, demonstration days and other events. Also there is a biomedical eng. faculty where you can collaborate with their experts and facilities. You will find plenty of people from your city there as well. Cost of living and studying is very good. You will have to do a 6-month pre-master trajectory before entering the program so this will be the best time to send in a letter, so the staff has time to review it before the crazy new season starts again.