I can tell you how I deal with it, although it may not be the solution for you.

I got overwhelmed by all the poverty and inequality in the world, and I thought, what am I good at that can help? Well, nothing really, but I could GET good at something that can help. So I took a (free) class in teaching adult literacy and now I do that a few hours a week. It really helps to know you're doing something about the problem and not just worrying.