First, I'm sorry for your situation and your axolotl, it really sucks to have a sick pet
this is what i would do:
1 - remove all of the rocks from your tank and only have sand or nothing.
2 - put your axolotl in a dark plastic container, with some tank water, in the fridge (make sure you leave an air pocket). There are some good fridge tutorials on the forum, take a look around. It will help him pass/vomit the rock if it is at all possible. And if not, keep him alive for longer (sorry). Leave him for a week or two before proceeding to the next step, to see if he can pass the rock on his own.
3 - suck it up and take him to the vet. You bought this pet, and in doing so took on the responsibility of paying the money to care for it if it got sick. It is very expensive, i sympathise, but if it is really as big as you make out - this is probably the only option to keep him alive.
4 - if he lives, read into proper axolotl care so emergencies don't happen. The easiest way to avoid the vet bill is to keep them safe to begin with.
I really hope you are feeling OK, and all of our best wishes to your axie. It will help if you take some photos for us? post them in this thread when you can. Good luck guys!