I can totally relate to your thoughts. I too, sometimes get exhausted or burned out just by thinking about all the things I am doing/wanting to do in life.
We are limited by the energy and the time we have. So doing everything that we aim for is almost impossible. But what we can do, is focus on a few things that are the most important for us and manage our time/energy for everything else accordingly.
For instance, I prioritize my internship, academics and personal learnings and spend time with things that I love - cinema, books, music accordingly.
While doing that I make sure that I am getting proper sleep, doing some physical activity daily and if possible meditation. You can add other things that make you happy.