Hi,
Thanks for your private message. I am not sure if I responded too late but I hope your axolotl is still going well. It will be worthwhile to first check that it is still alive if you haven't done so.
What you can do really depends on whether you have access to a local vet and how much you are willing to spend. If you can take your axolotl to a vet, I would recommend asking your vet to provide some anti-inflammatory and analgesic which will relieve any swelling and pain. Personally I use meloxicam quite successfully with axolotls. With pain relief and controlled inflammation, all it requires is time, good nutrition and water quality for your axolotl to heal on its own.
If the above option is not available, the only option is to use modified husbandry (axolotl keeping) to try aid its natural healing. With immediate injury (1-3 days), I would fridge the axolotl, keeping it cool and in the dark without disturbance to prevent secondary infections from the physical trauma setting in. This is the period when it will be most susceptible to secondary infections particularly if there is a breach to the skin. It will also provide some level of additional comfort for the axolotl. Don't worry about feeding the axolotl at this stage. Metabolism is slow when fridging (hence healing also slower).
After 2-3 days, depending on the state of the axolotl, I would consider moving it to warmer waters (around 16-17 degrees Celsius) with some added aquarium salt. The water temperature will still be cool yet warm enough to increase the metabolism of the axolotl higher. This promotes feeding and also wound healing. This is the time when I would offer it easily digestible and nutritious food (earthworms, pellets, blackworms) to aid in its recovery.
Regards