I think you may be on to something regarding the blockage. I know it sounds odd, but perhaps her rectum is tight. My oldest sister had similar difficulties (when she was a bit younger than your daughter) and my dad says that the pediatrician simply slipped on a glove and used some lubricant and carefully inserted his pinkie into the rectum and made a few slow circles of the rectum, and ta da! She started having regular bms and eating better. You can try this yourself, or if you're nervous about it, try using a lubricated q-tip. This is one of those very typical things in babies that younger pediatrician miss because we have lost sight of some of the most simple remedies that our grandparents used. Yes, I am a "mature" mommy, being 44 and my only child is merely 3, so some of the old fashioned, simple things in life have been handed down to me from my old parents, LOL. And if she is constipated, try some straight apple juice, not watered down, and give her about two ounces, maximum. Our pediatrician recommended this for our son and he explained that the full strength apple juice works because the natural sugars pull water into the bowel, thus resulting in a softened stool, and easier passage.
That said, if she won't eat from a spoon, which I'm sure you know is not unusual for so young a baby, try dipping your pinkie into the pureed food and feeding it to her from your finger. My son was unwilling to take a spoon for the first month or so when he went on solids. Perhaps she has a minor deformity in her mouth structure. My boy has a slightly shortened frenulum and a bubble palate, which made it difficult to nurse, and then a bit difficult for him to eat solids. Using the finger method, with the puree on the pad side of my pinkie seemed to help him with the solids.
I also suggest trying a variety of things until you find something she'll like. I made my son's first foods, and he ate purees for a long time. Our pediatrician told us to start with the yellow/orange foods first, like winter squashes and sweet potatoes. I would roast these things until they were VERY soft, then puree them. When you roast these veggies for a long time, they become quite caramelized, sweet, and tasty! You might try avocados and bananas as well. There is no set order of what solids to start with, only suggestions.
Good luck, and I'll be interested to know how things go for your daughter.