Your nitrite reading is 5ppm? That is very dangerously high. I would remove your axolotl from the tank and place her in a tub of fresh, cool, dechlorinated water and maybe offer her a black tea bath to soothe the skin. I would keep her in the tub until you can sort the parameters out in the tank and get it cycled using a fishless cycling method. Whilst your axolotl remains in the tub, you will need to change 100% of her water every day. An easier way to do this is to have a second tub pre-prepared next to her tub each day so you can simply transfer her to the new one and replace the water in the other tub with fresh dechlorinated water ready for the next day. You can dispose of the old water by adding it to your tank to help feed the cycle.
It seems something has crashed the cycle and it is in the process is of cycling again. May I ask what the issue is with your filter?