How can I make myself mature emotionally, or better regulate my emotions?

Whenever I'm faced with an upsetting emotion or situation, I often just continue doing the thing that's making me upset instead of just stepping away to calm down or switching to doing something calming. It's a detriment to myself and the people around me.

I also have another problem that's difficult to explain, but I'm going to try. Whenever I make a mistake, no matter how massive or minuscule it is, I just say 'sorry'; using it like a toke and a shield instead every situation. I want to stop doing that, and I want to actually own up to my mistakes instead of just making hollow promises over and over.

I need to figure out how to curb this behavior, find a healthier way to process my emotions and actually atone for my mistakes. Can anyone help me?