J.M.
First of all, I know how incredibly frustrating this can be.
Secondly, can you get someone to come and give you some relief (partner, parent, babysitter) for just a little while. I found that getting away for a little while really made things so much better for me.
Third, try to take a minute and figure out how much of this is frustration over the nap thing and how much is it the non-napping plus the incredibly hard transition to being a mom. I didn't realize until after the fact that I probably had some post-partum depression because I had such a hard time adjusting after my first daughter was born. I just wanted to cry all the time. At the time, I thought it was because of the baby and those difficulties, but now that I have two I realized that a lot of it was me. Doesn't make the nap issue any easier, but if you are really starting to feel over the edge, it's worth talking to your doctor or therapist about.
Finally, I would stop letting her cry it out (unless you just need a little break to take a shower or eat or something). She's really still little and it's normal to need some help sleeping (and I am a believer in c-i-o when kids get a little older). I think that the best thing that kids can learn from the get-go is that sleep is a good thing. So at the beginning you want them to associate it with being loved and held and feeling good. Then when they get older and can learn how to do it themselves they don't fight it as much. When she falls asleep, try getting her down into her crib. If she wakes up, muster as much energy as you can and greet her with a smile (this is the hardest part). Try getting her to sleep again when she seems tired and well fed (maybe only an hour later if she only napped for 10 minutes). The more she learns that sleep is okay, the more she'll be willing to do it.
One other thing - maybe mention to her pediatrican that she's having such difficulty. If you are comfortable, suggest a breathing monitor so she can sleep on her belly. We let my second sleep on his tummy and our house has been a much more peaceful place. After all, you'd wake up quickly if you were really uncomfortable and couldn't move too.
I'm sorry I wrote so much, and I really do wish you the best of luck. This part of motherhood is not fun. Try surrounding yourself with cute pictures too so that you can remember the good times when you are holding a screaming baby.