Yes, likely the weaning will help. It will also allow you to be more comfortable when you don't accommodate her by picking her up. It's definitely a 'bite the bullet' strategy but it will help her. You're the mother, so it's not surprising the behavior is occurring only with you. Realistically, you can't keep picking her up and holding her each time she cries, so weaning her from that practice (as well as from breast feeding) will be necessary. And, in the process, don't worry that you'll be doing her any harm in an emotional sense.
It sounds to me that she simply isn't emotionally ready to be done breastfeeding. I had a hard time with my little girl when she was about 18 months and I tried weaning her. I absolutely hate BFing, and tried to push the weaning along on my own terms without considering her needs and feelings. She just wasn't ready. She was acting the same as your little girl is. She's 2 now and starting to taper it off on her own. It's also so much easier for me to reason with her. I had a hard time accepting the fact that I had to nurse her until she was done or she'd be misserable, but that's just what I had to do. I think, as parents, we sometimes have to put off our own needs and wants to get through certain stages of our children's development.
Educating myself on the subject has helped me out so much. As you may or may not know, World Health Organization guidelines state that breastfeeding should continue for at least 2 years, then (after that) until mutually desired by both mother and child. That is also the guideline that the Amarican Academy of Pediatrics refers to. I've also seen it guoted on formula websites (since I have done research through them in order to get a biased opinion on the subject since, obviously, they would prefer you to buy their produst, which would go against BFing). Now, I'm not a complete boob nazi that believes you absolutely have to BF for that long. I think it's awsome for any mother to do it for even the first 6 months, since most mothers either won't give it a chance or quit after a few weeks. But I do think it's important that you make sure your baby is emotionally ready to give up that part of you. Because it's not just the milk your baby will be giving up. She'll also be giving up a special part of you that she has grown to love and has made her feel safe and secure for the only 14 months of her life.