I think you should try the pacifier a few more times. Baby can smell you and feel the softness of your boobs so they will search for it once they are very near to it. Biting down your nipple sounds painful but you have to bear with it and when they are drifting more deeply asleep, you can try to unlatch itch the pacifier and slotting it in immediately - that s what I did for my Son who was like your girl. Latch. Fall asleep then try to sneak nipple out. Although this is a passing phase you can consider trying to see what are your child's other soothers, like if baby is ok to hug a toy with your scent to sleep or to suck thumb. Different baby different soothers. Jia you. My boy use to latch to sleep, now at 6 months he doesn't really do it so regularly anymore
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!