The pain does stop when the tooth comes in, and yes, it does happen for every tooth. I think that the first few times seem like the worst, though, at least in my experience. (Maybe because its new to you and the baby...)
Have you heard about allspice necklaces (to use when baby is awake and attended)? I didn't hear about them until it was too late for my girls (just heard about it from some savvy moms). The allspice has tannins in them that make the gums more brittle, and the teeth pop through. The necklaces smell great, too, and can be soothing for babies.
My daughters never chewed on the cooling pacifiers for long, but loved little washcloths lightly wet, and stuck in the freezer for a little while. I also thought the Nyland's Homeopathy teething tablets helped a little, but not on a regular basis. We tried frozen waffles and teething biscuits, too, but I was too worried about them choking on the little pieces that inevitably break off.
As stated above by others, all babies are a little different.(My second wanted to nurse MORE when she was teething, because it soothed her, although she would occasionally try to teeth on me). I like the recommendation to be sure she doesn't have an ear infection, too, although given your babies age and what you said, it sounds like teething. They can run a little low grade fever, and be miserable with teething, but shouldn't be as sick as with an ear infection. Like another mom said, if she is miserable when she lies down, consistently seems to have some kind of pain when she's nursing, shakes her head a bit, and has a fever, best to rule out an ear infection. (That being said, one of my daughters would present with ear infections after having nothing much more than a fever, no "classic" symptoms. They're different!)
Be patient and as empathic as you can- sometimes teething lasts a long time (or seems to when one tooth is coming in right after another). Take heart- it won't last forever. :)