Oh honey - I could have written your exact post three and a half years ago when Jack was born. Very, very similar. I had an epidural, and his head was stuck crooked, but he was much smaller than your your lovely little chubs :), only 7 lbs 7 oz. Regardless, yanking him out with forceps after I'd pushed for four hours did the same kind of damage. Third degree tear (one surgeon afterwards queried wether it wasn't approaching a fourth degree tear, but then he said what did the numbers matter, the damage was horrific :(), massive blood loss requiring transfusion. Altogether a completely shit experience.
I'm so sorry this happened to you. Personally I believe they should outlaw forceps. There has to be a better way. But before I start on my rant about how IMO a birth that's clearly going pear-shaped should not be allowed to continue until both mother and baby are distressed, that we have the option of surgical intervention and, no, it should not be exercised arbitrarily, but neither should it be withheld until a situation is ridiculously compromised... umm, well, there I go ranting again 
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Ok, so back to you - from my experience, I would say at a week post-birth, your situation looks very hopeful. I had the same issue with urinary incontinence. Absolutely couldn't tell if my bladder was full, empty or at the half-way mark. Bladder? What bladder? I may as well not have had one for all I felt the damn thing. But the feeling does come back. Especially since you're so young and otherwise, I hope, healthy? I'm not saying that in a "pat, pat, there, there" kind of way - you have a huge advantage being 23. I was nearly 39 when I had Jack and there is a world of difference in the healing abilities of a 23-year-old vs a 39-year-old. And - this was never anything I thought to ask about, and god, I have a crap-load of medical eduction - women who've had lovely normal births, 9 hour labours, no tearing, have that "where the hell is my bladder" feeling! So... what I think is happening is that your nerves are shocked, especially the pudendal nerves which sit right inside the pointy pelvic bones that baby has to pass by (the ischial spines). If baby has a big head (and I imagine a ten-pounder would) and you had shoulder dystocia, then one or the other pudendal nerve would have been compressed between the head and the ischial spine, and taken a real beating. Possibly both. And from the trauma of the tear and subsequent repair, all your tissues down below will still be swollen which further compromises nerve supply.
It will come back. You may have to be very patient, but it will come back. I had what my GP calls "urge incontinence" for a very long time. It's not like stress incontinence where you leak when you cough, I never had that. Urge incontinence is when you have to go, and at the last second, you can't quite hold it, you literally either lose a few drops or start weeing as soon as your bum is lowering towards the toilet.
It's a good idea to do your pelvic floor exercises, but remember that your tissues are still healing. In my profession, we frequently disagree with physios because they push exercise as soon as possible, and I think that you need to support healing before you can exercise. But that's a professional disagreement and there is validity to both points of view.
What I'm trying to say is, even if your PFEs aren't too successful right now, they're helping you identify what feeling you do have and where, in other words, how your body feels now, after this trauma. So when the feeling comes back, you'll be in a better position to properly strengthen those muscles because you'll know where they are! :)
(((((HUG))))) - what an awful experience and what a shit way to begin motherhood. I think any of us who have had traumatic injuries during a birth are completely entitled to feel ripped off because that's so not how you think it's going to be. We all anticipate feeling tired, a bit sore, overwhelmed and a bit scared of the responsibility of taking care of this new life, but nobody expects to be doing it feeling like they've been bayonetted down below, and dealing with the fall-out of a very bad physical injury.
I've had some utter caaaaahs tell me "well, it's all part of childbirth", and I'm sorry but no, it's not. Nobody would expect a new mother to be up and around and fully functional if, say, she'd just had shoulder or knee surgery or been hit and broken a couple of ribs. Just because the injury is to a mostly-unmentionable place, doesn't mean it's any less incapacitating.
Holy cow, I must be in a ranty mood this weekend - that's two massive posts in two days!! What's gotten into me???