Absolutely. justKate, you wrote my comment. :)
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OP, my son was just like that. And because many other moms have told you of their similar experiences and solutions, I won't go into details about my own--but I just wanted to add that my son could become very upset his first month or so when I was in the shower, and he's become a perfectly awesome, well adjusted toddler. I know it feels wrong and tormenting to let them cry…but I also know now with perspective that you're not doing yourself a favor freaking out about it. Most likely, it will just have to happen for a little while, unless you find that elusive method that soothes your child. In the last two and a half years, part of my tribulations and trials in mothering has been balancing time for myself as well as my child. Unfortunately, in those first few months, it can be very hard to not be attached at the hip to your infant and to balance an AP style of parenting with your own sanity. I just wanted to let you know that this passes, and then it's as if it never happened…reading your post was like reading a diary entry from decades ago, I would have never remembered otherwise!...which should encourage you that letting your child wail for a few minutes will not traumatize them. When they get older, it's easier to find methods to help them soothe themselves, but right now, you will probably have to use the only half effective vibrations of the bouncy seat and the gritting of your own teeth to get you through. 
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Do you have a bouncer with a vibrate button? Or a vibrator that could go under the bouncer, a la Sex in the City?
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Can your DD see you when you're in the shower--like a clear shower curtain or glass door? How about if you sing loud silly songs (or just make silly noises/faces at her from the shower)? She's so young, that might not work, but it will later....
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I know exactly where you are, because my DD was this way too. And honestly, nothing worked for her. I just took really fast showers, with her in the bouncy chair watching me. I tortured myself over it, but she was only crying because (understandably) she wanted to be in my arms, and the bouncy chair was a distant second choice. When baby is right there with you, can hear your voice reassuring her, see you nearby, is fed, warm, dry, and safe, it is okay for her to cry. It sucks to hear it, because you're mama and it hurts to hear your baby cry. I think this is a pitfall that AP mamas get in to, and you have to avoid it so that you can avoid burnout. You might not be able to keep her soothed while you shower, but she is not scared because you are there, and your voice is there to reassure her. You just have to do it mama. Get baby situated in the bathroom close to you, and take a shower. Take care of yourself and everyone will benefit. 
