I relate to you very well. Since I was little I also felt very connected to the people in pain and suffering, but it has become overwhelming. I also have to deal with Depression and the world has too much pain for me.
I have learned that this is not healthy, and this is not what God wants.
Compassion and joy need to be toghether, because the main purpose of our lives is to live, and to live with abundance.
There are chemical inmbalances in the brain that produce that tendency to sadness and lack of hope. Lack of some aminoacids and neurotransmiter produce that.
We need to fight that. We need to have a healthy diet, have the vitamins and minerals our body need, exercise and do everything we need to do feel better.
Of course, the main key is to ask God for guidance, and to ask for the joy of life.
We can still have compassion for others, but it needs to be healthy and productive, not depressing and unproductive.
I encourage you to find the physiological reasons why you have this tendency, I know I have estrogen dominance that produces PMS and low serotonin that produces depression. I have been affected for sadness, anger, etc, but I know I can recover. And as long I try to get better, God supports and helps me.
I am fighting them and I have found help form wonderful people here in Curezone and other places that have been very helpful.
I am sure you can overcome this too, and be happy and productive.Pray for guidance. The world is also beautiful, just go for a walk and look and the trees, the animals, the sky and you will see how beautiful the creation is.