1991 Toyota Corolla My newly replaced half-shafts semi-popp

I just replaced both half-shafts, the tie rod ends, the brake pads, and the rotors on my car. I drove it a few miles, here and there, and it felt. Sloppy. Also, when I turned too sharply or too quickly, the driver's side tire squeeled. I figured I needed new tires and an alignment (the tires are pretty bald, and I figured an alignment would be appropriate after replacing the tie rods and since the car hadn't had one since who knows when). However, I was going down the road at about 25 miles/hr when my speedometer shot up to 50 miles an hour while my car began to slow. There was no loud noise, nothing. My car just began to act like I had just slipped it into nuetral, which of course I had not. I took my foot off the gas and the car slowed almost to a stop. I put it in park and it made a loud whirring noise, then a mild grinding noise (almost like a bad shift in a manual tranny car would sound). I pushed it home, about a block away. When I jacked it up, the half-shaft had come partway out of the tranny on the driver's side, and it even looks like the shaft on the passenger side came out a bit too. At most, maybe 2 or so inches. Tranny fluid had sprayed all over the underside of the car, and there was a trail on the ground. I tried to get the new shaft back out, but it broke off inside the inner boot and I cannot get the dang thing out!

I need to figure out what happened and what I can do about it! Did I somehow not put the shafts in all the way? Then why was I able to drive it around for a couple of days? Why does it look like the passenger side popped out a bit too? If the shaft is not engaged in the tranny, why won't it come out? How is that little clip that strong? Also, the car rolls when in park, so it is not engaging the tranny. Did the fluid just get flung around when the shafts popped out or did I blow something out? Did I get the wrong shaft? I checked the size, but I didn't count the little gears or anything.

Any help would be greatly appreciated! And I am doing this work in my driveway, no fancy lift available!

Thanks, Sara