BEEN THERE! It was driving me crazy! Bottom line - having her hold it and be backed up is NOT worth it! She could end up with encopresis which is really yucky and could be damaging to the bowels. Sorry this post is so long, but maybe our story will be helpful:
My daughter - she trained in 2 days at 2 1/2 yrs, no problem peeing in potty, went right to underwear, but wouldn't poop in the potty no matter what! She wanted a pull-up and would only go in one. UGHHH! I tried EVERYTHING, bribes, rewards, etc. I went back and forth between "no pressure, honey" and "this is gross!" but it didn't matter. Every time I tried to encourage her, it ended up in a fight. Easier said than done, but I bit my tongue and backed off.
She would never really articulate "why" and I think it was some fear, but also some stubbornness. One of the big issues was that she always pooped standing up and really wasn't comfortable sitting. We tried major and minor bribes and nothing seemed to work. She would cry and scream and have such a fit! She never pooped in her undies, though. She would hold it forever. So the idea of just "not giving her a diaper" or saying "we ran out" didn't work for us. She'd hold it for so long that we'd end up with a very constipated kid for days.
First, we said she had to go into the bathroom - that's where people poop - not grunting in the corner of the living room... (why do people let their kids do that? lol) She would go to the bathroom, I'd help her put on a pull-up and she'd stay in the bathroom and do her business. So she had to miss out on whatever else was going on - playing, etc. She was not allowed to wander around in that diaper, going when and where she felt like. I'd clean her up and then put her back into underwear - done.
We then gradually worked on SITTING on the potty (in the pull-up.) We wrapped up about 25 small presents (playdoh, markers, little toys, etc) and every time she went sitting on the potty with the pull-up, she got to pick out a package. She knew that when the presents ran out, it was time to go without the pull-up. She really wanted a "real" camera, so we said she could get one the day she pooped in the potty. When that day came, she was very upset and cried and didn't want to, but I stuck to my guns. After she did it ONE time, that was it. We bought the camera and never had another problem. It wasn't worth having her get horribly constipated and in pain. I'd rather she go in the pull-up than not go for days and days.
I've also heard of people using this tactic and then cutting holes in the pull-ups, so they'd wear it and sit on the potty and end up going IN the potty, "wow, honey, look at that! what a surprise!" Sorry to say, this went on for nearly a year after she was potty-trained! But once she finally did it, she never had an accident and never had a problem after that. I have known and heard of lots of kids with this pooping issue!
She's now 5 1/2 and has never had an accident and has no issues with the potty. I look back on that time and cringe at how angry and upset I'd sometimes get! Try to back off and allow her to be in control; give her a pull-up to poop in (in the bathroom), but make it clear that pooping in her undies is not okay and keep her in underwear the rest of the time. All the best! You'll both get through this! P.S. - my son was a breeze, totally trained before age 2, no pooping issues, easy-peasy!! I think it's more emotional with girls.