These cords are called "Etheric Cords". They are psychic cords that form between two people that are like hoses. Usually they dissipate after a short time. I was researching them, and came across something you might find useful to cut them. Read the article to determine the type of cord you are attached to, where the pain or energy drain originates, and how you wish to proceed.
Good luck to you!
I ask my angels and spirit guides to help me in this task. I wish to free myself for all eternity from ___(name)___ so that both of us may go free from ties that bind and all energy attachments from the past. It is time to move past the experiences we have shared. I am thankful for what I have learned and lessons given, but this attachment is no longer needed and is holding me back and affecting my 'now'.
With power I now ask for all cords to be cut, for all energetic cords physically connecting the two of us to be removed, dissolved, transmuted and cut free, and all energy to be returned to the original sender.
It is my intention that no more energy attachments hook onto me from ___(name)___. With forgiveness and peace I release them to move away from me and move on whilst I do the same.
I now call upon Archangel Michael to use his mighty blue sword (or Sananda, Saint Germaine, Kwan Yin, Mother Mary) to surround me and cut away the cords and give me protection. I ask that this be complete and sealed NOW. Please cleanse my aura of negative energy and emotions, and seal it with love. Amen.