No offense, but you people aren't helping this girl out. Distilled water is bad because it has absolutely nothing in it. It removes stuff like metals and dirt, but it also gets rid of the minerals, that's why it was recommended to add some. Water conditioner does not add minerals to the water, all it does it neutralize chlorine and chloramine. If the water has nothing in it, then of course it would not have chlorine, chloramine or ammonia. Stress coat doesn't do anything for an axolotl because they don't have a slime coating, I've actually seen situation where all it did was irritate the axolotl's skin. Also, that link to axolotl.org, though, yes, that site is wonderful, it doesn't help in this situation. The different water solutions also don't add minerals. Those are for treating and preventing different axolotl diseases. I utilized some myself and know that most of them just use salt, baking soda and few other things.
If your tap water is a problem, use spring water or betta water. It's expensive, but it's better than distilled. Also, the point someone was making before was that there is no reason for you to put the axolotl in the tub because you already have the tank. Cycling a tank doesn't happen in a week, not even two weeks in most situations. It usually takes around a month or more. Furthermore, as someone pointed out that they never cycled their tank. Well, that's because ammonia isn't as toxic in lower temperatures and at a certain point doesn't even get processed by the biofilter. You should just put the axolotl in the new tank now. There's really no reason to have him sitting around. You're also not going to cycle a tank with old aquarium water. The only way you would be able to contribute to the cycle from the old tank is it add the filter, but you have a new one anyway.
I'm currently having a problem with cloudiness in my water too, but my parameters are perfect and I have a cycled tank. Therefore, this is no cause for alarm. Just because the water doesn't look clean to you, doesn't mean it's not, so don't panic. You should be doing the largest water change you can do once a week. Otherwise, two small ones twice a week.