I could have written this post about my eldest. I remember how hard, how really hard it was.
It does get better!
It just may take awhile. Like you said, this is a tough time, with lots of changes, and the dreaded molars. My girls always had a hard time with molars, and we often had to use Motrin at bedtime. Watch your little one, because teething pain makes falling asleep very difficult, even if it doesn't bother her during the day. I know it is frowned on around here, but the only thing to worry about with motrin is 1) correct dosing and 2) something in the tummy - nursing is perfect, and sounds like you are doing that anyway.
My DD was a completely different child once all her molars were in; all our sleep issues changed after that.
(And just to really hold out the hope for you, she then gave up naps and was good for 12 hours at night!!! I never had to fight with her about bedtimes as she got older. Now, at 10, she sets her own bedtime and sleeps very well, although she has never been able to go back to sleep - once she wakes, she is up, even at 6 am.)
One thing I have learned is the "sleep window" - they have a short period of time where it is fairly easy for them to fall asleep (aside from teething pain...) and if you miss that window, it is then very hard for them to fall asleep! If she has yawned twice, she needs to be falling asleep - by the third yawn, you are in danger of missing the sleep window. Don't pay any attention to the clock, just watch your child. For instance, my nearly 3 yo still naps starting between 10-11 am, for 1 1/2 to 2 hours - nearly every other child I know, including my older two, take an afternoon nap at this age. But she is ready to sleep before lunch (hmm, maybe from waking at 5:30 am?) and if I miss it, she will be crabby, then nap just before supper, then be a bear to get to bed. So you have to really watch your DD, what are her patterns, what are her sleep cues that tell you she is getting drowsy? Really watch her, she will probably be ready to nap by 4 hours after waking. Getting a good nap is crucial to falling asleep well in the evening.
The night waking is developmental, sleep rhythms are about 3 hours. That will pass. I know how exhausting it is. What helped me was actually just adjusting my life, and my mindset, and not planning on getting things done once she was asleep. Since my DH worked nights, I shouldered bedtime too. In fact, I can probably count the nights I have been away from the house in the evening in the past 10 years. It is just a commitment I have made to my kids - but that doesn't mean I always like it! But anyway, instead of thinking "if she would just sleep, I could...." and just try to be very zen about being in the moment of going to sleep. Many times, I just made it "our" bedtime, and just got things done during the day. At least I got more sleep, even if it was broken.
Which, since you are doing so much parenting alone, it is really important that you get support and some time alone to recharge somehow, whatever fills you back up. I found it at La Leche Leage, which led to AP playgroups, and at MOPS. I also am blessed with family willing to help. Seek out those sorts of like-minded mamas or others you trust to spend time with your DD so you can have a break.
Book recs - E. Pantley
books might be helpful, and I love Dr Sear's Nighttime Parenting
Hope this helps!