I think this is very common for babies who are breastfed and not on pacifiers. My child was like this too when she was younger, I had to bf her to sleep and she outgrew it around 5 months. Like the mummy above said, its a phase, they will outgrow it. If you don't want to practice such attachment parenting, you may want to let her fuss for a period until she get used to it. Pacifiers never worked for my child, she did end up sucking her thumb for a while and also did outgrew it around 6/7 months. Remember that she's still very very young at 3 months, and your boobies is just looking for a way to feel secure and comforted. Hang in there!