5 degrees Celsius is the minimum temperature for using the fridging method. I don't think fridging is needed at this stage, since your aiming to feed more, and fridging will reduce appetite. Keep trying to feed and hopefully he will get back to normal.
Exactly which Seachem product are you using? Is it just called 'Prime' ?
How you been doing any water changes in the main tank?
It would be best to remove your second axolotl and place it in a similar setup to your 'sick' Axolotl. Then begin adding food to your tank to create ammonia. A less messy way is to add the food to a tea bag, I make a slice in the tea bag, empty the contents then fill with the food, also threading cotton through the tea bag to tie it down. Otherwise, just purchase pure liquid ammonia, a couple drops would rise your ammonia, saving you the time of waiting for the food to degrade.