You sound like you are describing my first son (now age 2). He was breastfed on demand and started teething at 4 months- and would not take a pacifier. What I figured out was that the sucking was soothing to his teeth, and there were many nights that he nursed off an on all night, every 2 hours. It was exhausting, but was what he needed at the time- (he never acutally slept through the night until after his 1st birthday). I know it's frustrating when your child used to be able to sleep through the night, and now wants to eat all night long, but my advice is to let her eat. It probably makes her feel better, and the close-ness to you is probably very comforting as well. Signs of teething include lots and lots of drool, unexplained crying or fussiness, sometimes a low-grade feever, and sometimes diareah. If your baby is uncomfortable due to teething I would urge you not to "let her be" but to try to help her feel better. You will be very tired from your sleepless nights, but maybe you can try to get a nap in when she naps during the day. You will have plenty of time to work on getting her to sleep through the night as she gets older, but working on it while she is teething might be bad timing.
With regard to the teethers, I was able to get my son to use a couple. (His favorite looked like the fisher price deluxe gum soother, but without the hard plastic piece to hold.) It seems like the softer and smaller teethers are easier for them to get into their mouths. You probably already know this, but the first teeth tend to come in in the center of the bottom. If your baby has unexplained crying and you think it's the teething, try using the teething gel (medicine). Baby Oragel makes it in a swab- kinda like a q-tip. It is much easier to apply this way. The relief doesn't last a really long time, but when my son was really teething it was perfect to use and by the time it wore off the tylenol had a chance to kick-in.
Just my thoughts, Hope this helps!