Don't take on the anxiety of others. There is nothing wrong with deciding that your mother, father and siblings problems are not something you need to feel anxious about in yourself. You can show concern for them and try to help, but build a wall so you don't take on their anxiety. You are not responsible for making them happy or solving their problems. We have enough anxiety to manage for ourselves. I have this same issue of worrying too much about others.

For emotional outbursts of anger, you might want to pay attention of what words or situations trigger the outbursts. The more you are aware, the better you can recognize when they might happen and try to stop them.

I am happy you feel better after meeting with your therapist.