Transmission issue or speed sensor issue?

The truck had been driving fine until a radiator hose blew a couple weeks ago. We replaced the radiator (it had a very slow leak) and hoses. I drove it to work 2 days later and, on the way home, I stopped at a light and when I went to go it wouldn't shift out of first gear, RPMs would go to around 3,000 and the speedometer needle was bouncing. We replaced the speed sensor after that. I drove it to work again the next day and half way to work I stopped at a light, and it down shifted really rough as I was coming to a stop. When the light turned green, I accelerated and same thing as before, it wouldn't shift out of first gear and the speedometer needle was bouncing. I limped it in to work and upon further inspection the dipstick tube for the transmission has broken off. Presumably from the hose blowing the week before. We called a transmission shop, and they said they didn't even need to look at it, it needs a new transmission $5,000. So, my truck is still sitting at work and I'm skeptical.

Could it be that the speed sensor is faulty again? If so, what could be causing it to happen so fast after just replacing it? Or is it really that the transmission needs to be replaced?