.5 gallon and 65 degrees? Well she's way too cold, for one thing, and doesn't have enough room to move, which might account for her spastic movements. Did you condition and let set the water you put in? How hot was it? You might have burned her. It's never a good idea to heat a tank with a cup of hot water. It's not going to help in the long run, and you might burn your fish.
If you can't put a heater in the tank, keep her in the warmest room in the house at least, and I think it's time to invest in a larger tank and a heater if you really do want your fish to stay healthy.