Yeah, mindfulness is good for about anything, well, as I understand the main idea around it is to live in the present moment, not in our mind. I used to meditate a lot but lately since I'm depressed I live too much in my mind.
What helps a lot with not being swept away by others' emotions are grounding techniques, you could look these up online, and yeah, what I've found really helpful is to do a short body awareness meditation in the morning for example, and feel the parts of your body, like doing some kind of inventory, from the top of your head down to your toes. Or you can just focus on one part. There are many techniques, but to be honest, being sensitive like that will always make you be more receptive to your environment and if you are for too long in an emotionally draining environment then it will take its toll on you. Hovewer, if you find many ways to recharge yourself, it might balance it out, but in some cases it won't. For example I'm working in an open office environment and I got to a point where I realised that it's too overwhelming for me to work in such a place with constant stimuli and people around and now I'm having axiety issues.