Why am I internalising other peoples feelings and taking it out elsewhere?

For instance, I am new at my job. I am really really careful of who I become friends with but I can't choose my co-workers. I have to sit with my co-worker in my face 7 hours a day. And she must be on menopause because she has anger issues with almost everyone. And another co-worker who is the same. They go on and on and on about things all day long. Very loud people while I am shy. And while I was talking to someone by email I was being very very mean to them. I couldn't quite workout where this anger and meaness was coming from usually I'm quite calm. Then one day my co-worker was having an argument and she said mean things I said in this email. What is happening?