Your sanity and your ability to watch large amounts of news don't get along too well with each other.
You'd have to be overwhelmed by the enormity of humanity's suffering and your inability to do anything about it if you did nothing but watch and read news. Either that or you'd have to desensitize yourself to the point that nothing really affected you. Both are equally problematic.
Are we really strong enough to deal with a world where we have this much information about how people are capable of acting?
Yet we hear the exhortations over and over again. Engage! Engage!
Engagement is fine, but that engagement has to be attached to an actual ability to influence events. Engagement in an issue that you have no ability to act on is at its root an exercise in abnegation. It denies the place of the self, and the location of the self, and the ability of the self, all for an illusory feeling of connectedness.
Be compassionate for those whose lives are worse than yours. Give money to charities that help them, but don't let sorrow for their situation overwhelm you. There's an untold amount of suffering that doesn't get our attention, and there's an untold amount of happiness which we are left ignorant of. Neither are as important to our ability to live a good life as the forming of real, compassionate relationships with those around us. If we cannot develop within ourselves compassion for those sitting across a table for us, do we really believe that our compassion for people half a world away is heartfelt.
I spent a good deal of my early 20's addicted to the news. I knew that it was time to stop when I finally noticed that the life I was living and the emotions that I was feeling weren't my own. I was vicariously living other people's lives and feeling other people's reported feelings. The route to happiness and a good life can come through compassion and understanding, but it builds upon a genuine relationship with others and our own selves, not mediated experiences.
As my good friend, albeit 2000 years removed, Epictetus put it, everything has two handles, the one by which we can carry it and the one which we can't. I put in one of the first bits on this blog because it guides my thinking.
Disengage from those things which you have artificial connections with and engage fully with those things that are all around you, those things which you can truly engage with.
I don't advocate this as a simple selfishness; self-centredness doesn't bring happiness along with it. I advocate it as reality, as a building up of honesty and strength and decency in ourselves so that we can have the reserves necessary to deeply engage with what is important to us.
Engaging is not the first step of the dance, it comes long after the music has started. Being good at it requires training our reason, developing our perspective, and coming to an understanding of ourselves. The best dancers make it look easy, but you only see the dance, not the hours and hours of mind numbingly routine practice. Disengage for a bit, get that practice, and come back all the better for it.