In Medicine, your branch preference matters more than the institution. It is so because Engineering and MBA graduates are able to switch their domain, doctors have to stick to their specialty. 

It is suggested that you continue with MD general medicine rather than opting for MD emergency medicine at AIIMS Rishikesh. Here are some reasons why:

• Independent Practice (entrepreneurship), which is also possible with emergency medicine, if you have enough financial resources to come up with an ICU setup.
• Super-specialization in areas such as gastroenterology, endocrinology, neurology, cardiology, rheumatology, and even critical care (emergency medicine).
• Unlike emergency medicine, general medicine is a well-developed branch whereas emergency medicine is still in its very beginning in India. 
• Other specialties such as anesthesia, pulmonary medicine, several diploma courses from unrecognized institutes such as Medvarsity, ISCCM Courses, Master in Emergency Medicine (MEM), etc. compete for emergency physicians posts.
• Most of the critical care HODs are MD general medicine and DM critical care or FNB critical care.

The only reason to join MD emergency medicine is if you want to practice emergency medicine without dedicating extra time after MD.