It sounds like physical contact with her is a big struggle. What about taking her out for tea or to a museum, just you and her, on a regular basis? There are ways to make her feel special and loved that could be fun for both of you, even if you don't feel a particular bond with her. Does her father have any suggestions?

Do you have problems touching/being touched by other people or is it just your daughter?

When you do talk to that therapist you called, I would ask them if there are people who specialize in this kind of problem and get some names. You may need to interview a few therapists before you find one you're comfortable with.