Seems to me that you are exactly the type of client they are meant to serve. I've worked with a lot of women who survived horrific abuse, and many of them have said the emotional abuse was harder to heal from. Someone subjected to physical abuse might experience more raw fear than survivors of other types of abuse, but all abuse is damaging to one's sense of self-worth and value and confidence.
Trust me, if they feel their services are not a good "fit" for you, they will refer you elsewhere.