Dogg, I don't know about your tire; seems odd. I would agree, "if in doubt, throw it out". A head first crash, due to a bad tire or any reason could be the last worst experience.
As for the tube, I was having similar poor results. That is, the tube would fail right at the valve stem. The local bike shop thought the tires might have been a bit underinflated and the tubes 'walked' around and sheered. This made sense to me because I inflate to minimum possible pressure. Try just a bit more pressure if you continue with the same problem.