I'm still having problems with this stuff. I'm working on getting a full tank testing kit soon so I can tell you everything. Right now I only have an ammonia one. Would empting out the whole tank and washing it help any? Although I've noticed the algae is also in my filter.
Please DO NOT WASH EVERYTHING down - that will reset your tanks cycle completely & is NOT NECESSARY!
I think you might be mistaking slimy beneficial bacteria for algae.
What happens while you are cycling the tank is bacteria a needed to build up on EVERY surface - essential in the filter.
After a while this bacteria settles in & with regular SMALL DAILY WATER CHANGES - the bacteria will do the job of converting
Ammonia -> converted to -> Nitrite
NitrIte -> converted to -> NitrAte
NitrAte is the least toxic of the 3 & is easy to control with weekly water changes.
If you have an ammonia test - what is the current reading? How often & how much water have you been changing?
Are you using dechlorinator in the new water you add back into the tank? Which brand is it & are you careful measuring it out or just sploshing it in?
Please post a picture of the tank & your axolotl - just in case we can see something you might've overlooked.
<3 >o_o< <3