it sounds like she just wants to suck and suck. i would keep trying the pacifier. try a different kind maybe and just hold it in her mouth. (they usually spit it out all the time anyway...the only way I could dd to take it was to hold it in her mouth until she was old enough to figure it out on her own). have you tried to instill some sort of routine? that really helped with mine. she would eat about every 2.5 hours at that age, and take many many naps. you could also check for acid reflux. i guess eating actually makes their tummies feel better (as they're eating), so they want to eat and eat. I used Zantac for a little while with dd, but honestly, the real solution was in instilling EASY. It solved every problem we were having with fussiness and eating confusion and napping and night sleeping. it really was a lifesaver.
anyway, congrats on the new little one! you'll get lots of help on here. everyone's super supportive.