Hi Sharon,
It must be really distressing for you. I wish i could offer more help.
Based on the photos, i agree with the others that cloacal prolapse is top of my differential list.
Cloacal prolapse is multi-factorial, caused by a combination of factors including inherent genetic predisposition, diet, underlying pathology like impaction, constipation or growth of a mass around or in the cloacal region.
There are palliative conservative treatments that can help in minor or subclinical cases, whereby they may spontaneously self resolve.
The first thing i would consider doing is to refridgerate the axolotl under clean water conditions and offering easily digestible nutritious food.
To make food more palatable and easily digestable while still nutritious, i tend to feed my sick axolotl patients with a mash i make up myself. This mash comprises of moistened axolotl pellets, earthworms, bloodworms, shrimp, mussels, deboned -non white fish fillet, beef heart etc. that i blend together in a food processor. The resultant mash is doughy in texture. I then proceed to roll them into pea-sized portions before offering. I personally have good success with this method. The mash balls are attractive to axolotls due to the scent, are nutritionally complete, can be stored in the fridge easily, and best of all is highly digestable due to the pre-pulverised ingredients that increase the surface area for digestive enzymes.
In many cases however, cloacal prolapse would require veterinary intervention. I only had one experience clinically in practice whereby my boss (senior vet) reduced the prolapse by gently manipulating the prolapse back into position. In some instances, a fine suture may be required to hold things in place. That axolotl went on to recover uneventfully.
Best regards