How to balance trying hard in a Master's program with stress of working too hard and not having a life?
Emillie,
I to struggle with the same issues.  I am working on my Masters as well.  I have a few handicaps that make my life a bit difficult when trying to do my best.  When I ask my professors questions, I get, Keep up the good work, if you require more time, let me know.  Never the answer to what I am actually asking for.  Anyways, I strive for one day at time.  I keep my head up and continue to find enjoyment in small things, to keep my head from exploding on the larger things.  

Remember why you started what your doing now.  Pull your energy from your roots/background.  And focus on why you want to do what your doing!  What is your end game?

Try to get some exercise, specifically cardiovascular.  

Then start to eat the elephant again, one bite at a time.  

There are those who don't want you to succeed, and strive on seeing you fail, because that is one less person in the pool or class.  When you do finish, and you will, keep that in mind!  Be a motivator!

Good Luck, 
Ron