Laura is right, take your Axolotl out of the tank ASAP. Its being potentially exposed to extreme levels of ammonia, nitrite, and nitrAte. Take no chances, move your Axolotl to a separate container, I use large plastic food containers like this:
Then change the water everyday with dechlorinated water to make sure no ammonia builds up.
I wouldn't use any of the additional chemicals to bind ammonia or nitrate, Tetra AmmoniaSafe only detoxify's ammonia while you perform water changes, it does not remove it. You would be better to find the root cause of your extreme test results. Same with Tetra EasyBalance. You can easily perform water changes to lower ammonia and nitrate, then you eliminate adding additional chemicals to your tank. There's just no need for it when you can completely control your cycle your self.
It does seem that if all your other tanks in your house are giving correct test results then there is potentially an issue in your tank.
You need to establish whether the extreme test results are really true.
- Follow the instructions on your test kit perfectly to make sure you get true results.
- Make sure your test tubes are clean and dry before testing.
- Once you have performed the tests for ammonia, nitrite, and nitrAte place the tubes next to the color chart and take a picture, upload it to this thread.
- Take pictures of your tank/setup and upload to this thread.
But as Laura asked, how aware of the nitrogen cycle are you? Do you fully understand the process?