Cutting cords can definitely work.
There are so many ways, you simply have to find what works for you.
There are a lot of books on being an empath, and how to empower yourself. Check Amazon or other online bookstore and see what jumps out at you.
"Sensitive is the new strong" by Anita Moorjani looks fantastic. Haven't read it yet, but I've read a couple of her other books that I have loved and would recommend any of her books.

Books by Matt Kahn or Judith Orloff. I have never read any books by Judy Dyer, but her books are heavily promoted/advertised on Amazon (if you search for empath). I have to admit that has always turned me off a little, as a good book should stand on it's own without the heavy promotion that she and/or her publisher does. They might be worth checking out as she has a lot of them. I've just never been drawn to them.

One simple way to prevent yourself from taking on another's energy is to create a rose in your mind and put the rose between you and the other person. You could also place a big beautiful rose around you. If you ever feel the need for a fresh rose, blow that rose up and create a new one. By blowing up I mean just put it out there in front of you and watch it explode. That releases any stuck energy the rose may have accumulated. The rose will clear itself anyway, but blowing it up accelerates that process.
Just start the journey on empowering yourself and see where it takes you.

I wish you well.

Edited to add: Check out books on EFT (Emotional Freedom Technique). It is very simple to do and clears out crap (feelings, emotions, emotional pain etc) that you no longer want to affect you negatively.