Eating random things?

So, it seems that no matter how hard I try, I just cannot keep random bits of "stuff" from ending up in Princess' mouth. I try to keep her paci in (which Josh has pointed out we can't do forever), but if she really wants to taste something, she knows how to spit or pull it out. I try to watch her all the time (Josh suggested I don't let her on the floor if she is more than an arm's reach away! - then I would never be able to do anything!) I try to keep the floor vacuumed, but since our vacuum has been in the shop for 3 weeks, thats a little hard (ever tried to dustbust a whole living room?!) So in the end, she ends up tossing in a shred of carpet, a crumble of leaf, a piece of cat food, and any of a number of random bits before I can stop her, and then I have to hold her down and dig it out. I worry sometimes about what this will do to her... the things she is eating, and the process of me getting it out. It's never pleasant. Somtimes I just shrug and figure, kids have eaten worse, at least I got it out (but who knows what she swallows that I never see!) Yesterday I apparently scratched her gums (already swollen and sore from teething) while trying to retrieve a string of carpet. In the end, I prevailed, but her gums were bleeding. She cried, and I had to fight hard not too. I called Josh and he assured me that she was alright. It's bad enough when your children feel pain, but when you are the one who caused it (even when accidental!), it really hurts.
Does all this make me sound like a bad parent? I hope not! I know that anyone with kids has experienced something very similar. In the end I think all I can be accused of is being overprotective. I can just hear it now, "your such a first time Mom." But you know, I have come to see that as a compliment of sorts. Afterall, I am a first time Mom, and if that means that I wash my hands twice as often, carry baby wipes and hand sanitizer and disposable changing pads everywhere I go, and want the absolute best for my daughter, then so be it. I am a first time Mom, and proud of it! So you better take off your shoes at the door and wash your hands when you come into my house ;)