Nobody can't change the whole world, but you, as an individual, can make a difference. And making a difference isn't in the big things, it is often in the small things. The small things that people think that don't matter. Sometimes it is smiling to a stranger. Being nice with people. Telling the people you love that you love them, what they mean to you. Those seem like little things that don't make any difference at all, but they really do! The same way that little things like small insults, actions, that don't seem to matter can really hurt people.
So yes, I really think that life is worth it. That doesn't mean I don't havebad days, I do, the same way as you do, but those bad days you should remind yourself how great those good days were. If you think that way, the bad days won't feel that bad. And get the most of those good days, because small things, moments and good days, good moments are what makes life beautiful, worth living. Happiness is found in small happy moments :)