Welcome to my world!! Well my world 4 months ago anyway. My youngest went through this from 4 mos until 6 1/2 mos. The worst part about it was that she started sleeping through the night at 2 1/2 mos all on her own, then all of a sudden at 4 mo. she's up again and not just up once for a couple minutes, she's up for three hours! It was the same thing, I'd rock her and as soon as I put her back in her bed she'd wake up. She would only sleep if I was either walking with her or rocking her and I actually had to get her back to sleep before I could sit down in the rocker. I too thought it was teething, but Tylenol didn't help her either. I also took her to the pediatrician twice, sure that she had an ear infection, nope. I couldn't let her cry either because she would cry so hard she would make herself throw up. I don't have a problem with babies crying, we let our oldest cry herself to sleep many times, this one just couldn't do it. I know exactly how you feel. I was averaging about 4 to 5 hours of sleep a night and not in a row either, and I had two other kids, plus the baby to deal with the next day.
I bought this book called The No-Cry Sleep Solution (I can't remember the author right now, I got it a B&N on-line). It did help but I still think it was teething with my DD. I read an article on teething that said it's not really the tooth busting through the gum that hurts them the most. It's when it's moving up through the gum which can take a couple months before it actually pops through. My DD got 6 teeth in the time span of 3 weeks. After the last two popped through, she went back to sleeping through the night within two days. I'm not sure why the Tylenol didn't help, maybe it was just too painful and couldn't take the edge off for her. As she's gotten subsequent teeth, (only two more and they came in one at a time), she's had a bad few nights before they've come in. I think before she just had so many coming in at once it was unbearable for her. I think it's different at night because during the day they're busy playing, chewing on stuff, etc.
I did notice that you said that for naps your DD sleeps for about 45 min wakes up and then goes back to sleep about an hour later for 45 more min. Have you tried getting her back to sleep after the first 45 min? If she's going back down an hour later, she's still tired after the first 45. With my kids I noticed that if they were on a more reg. nap schedule, that helped their nighttime sleep alot. They all also have small fans in their room for background noise. I think this does wonders!
My best advice for you, especially since you only have one child is NAP WHEN SHE NAPS! Let go of the cleaning and the laundry a little bit. The world is not going to end if you have dust on your table or crumbs on the floor. This will not go on forever and you can then get back into your usual routine. If you're tired and crabby because of your lack of sleep, you're not doing yourself or your child any good. My SIL told me this when my first DD was born and it is the best advice I ever got. You do feel guilty about it at first, but trust me, I'm a much better mom when I've gotten my sleep.
Good luck to you and remember, this too shall pass, although I KNOW it totally sucks when you're going through it. Feel free to PM me anytime!