In fact, there is a shortage of professionals who are both Doctors and Engineers.
First, Please decide on what branch of Engineering you are passionate about and like to pursue, and/or what branch of Medicine you deeply care about.
For example, if you are passionate about Mechanical Engineering, you may like to become an Orthopedic Doctor, because of the synergy you will find.
Similarly, if you like Electrical/Electronics/Computer Engineering, you may prefer to be a Neuro Surgeon or Neurologist.
There are many Universities which offer accelerated Medical Education programs and allow subsequent specialization in Engineering. If you can get into a combined/accelerated program of any these Universities , you will be well on your way to become a Doctor and an Engineer.
Please do not worry about the time and other resources that you will spend pursuing this joint education & career opportunity. It will be well worth it.
You will be rewarded amply, in addition to contributing significantly to the society.
Looking forward to see you as a very successful Doctor plus Engineer, in future.
All my Best.
Absolutely! That would be great for yourself and the community. Medical engineering is constantly being developed and lot's of money is being invested in this area. A person with a dual degree would have a big potential both with research hospitals as well as in the medical industry.
The challenge is how to finance your studies over an extended period [expect 5 to 10 years in total] since it is unrealistic to get a higher engineering and medical degree in parallel. What I'd do is choose one to start with and complete that education. Then I'd do some work and start working on the second degree a while later, maybe at half time and work half time too.