With those parameters, I would suspect your tank is going through a cycle. If your filter was taken from a previously cycled tank I would think that your filter does not have enough bacteria to keep up with the ammonia being generated. I've never cycled a tank with animals in it, so I wouldn't know what to recommend. You need the ammonia and nitrites to complete the cycling but at the same time you don't want it at levels that will harm your axolotls.
On another note, did you say you had a 29 gallon tank? As a rule of thumb, axolotls require around a 20 for one axolotl and 10 gallons for each additional axolotl. It may get a little crowded for 3 full grown axolotls if they get up to 12" long. You're better off with wider shallower tanks.