You are not bad parents!!
My kids both loved tearing up catalogues at that age and quite a bit of them ended up in their mouths (with and without me noticing), but usually they just get soggy & eaten or spat out (sometime fished out as a soggy mess). I've not had either of my little ones choke on paper. It sounds very scary!
Gagging/choking is very scary. My ds choked on anything but thin pureed food til he was 10 months of age, so we had to endure terrible choking episodes every time I offered what was meant to be age appropriate food to him. It was very stressful.
You'll soon become an expert at putting your finger in your bubs mouth to retrieve all sorts of things. Babies explore their world by touching, smelling and tasting/putting things in their mouths. Hopefully it's the last choking episode for you, but it won't be the last time something goes in her mouth that shouldn't be there!