No worries sharon, anything for my favourite shazza. I thought i shall just answer your questions from your email here so that there is a case history link for easy reference.
Any vet would be able to perform a fine need aspirate. Basically the vet would get a needle and syringe and randomly take several random samples from the lesions by sucking up material from the lesion. This procedure is minimally invasive although analgesia and anaesthesia (ie. isoflurane) can still be used. I would tend not to go with anaesthesia for this as there are more risks associated with anaesthetic delivery. The most critical part of most procedures is actually anaesthesia.
Thereafter, the material (whether its cellular or a fluid discharge), can be placed on a slide and stained to look for microbiological agents such as bacteria and types of cellular composition (whether there are inflammatory cells, cancerous cells etc). This alone gives a lot of information. If bacteria is seen, the sample might be cultured to identify the specific type of bacteria and what antibiotics they are sensitive to. This would give the direction for appropriate antibiotic therapy.
The next step up is getting a punch biopsy. This is more invasive than the fine needle aspirate but again can give a lot of information. A piece of the lesion is removed for histopathological analysis. The necessity for this step is determinant on what the fine needle aspirate reveals.
To be honest, my greatest worry is that it is a form of cutaneous tuberculosis caused by mycobacterium. This type of bacteria infection are super nasty to treat because they can remain latent, highly infectious, can cross species and very drug resistant. Even some drugs commonly used to treat this in small animals such as doxycycline are not suitable antibiotics for axolotls. Tetracycline class of antibiotics cause nasty skin irritation, sloughing and even dermal necrosis. Dead skin ain't pretty. Mycobacteria infections often take on the clinical presentation of such type of skin lesions.
I would say that anaerobic or clostridial infections are much less likely, simply because the tank environment don't tend to support their growth. Unless there were prior penetrating wounds on the axie that seeded these bacteria types, it is less much less likely. They also tend to die off in highly oxygenated environment. There is still a remote possibility though as such infections tend to cause ballooning type lesions due to a gas buildup (crepitus).
The next possibility are external parasites and flukes. Some axies react very strongly to such irritation. They start having an overt immune reaction. Flukes or any burrowing type parasites in particular, can cause local inflammation to the tissue, much like how you get a itchy raised bump from a mosquito bite. The axie's body will try to wall off this foreign body by forming the lesion as a means to prevent it from entering deeper tissues or the bloodstream. Some parasites also adapt to this and actually use it to their advantage to proliferate. A fine needle aspirate and microscopy can help reveal if parasites are the cause. Once they are identified, the treatment is usually more straightforward.
In summary, the axie still needs to see a vet but if you are cautious, you may opt to just go for fine needle aspirate and assessment /diagnosis before jumping to treatments.
Cheers.