Fungus or algae?

[Caesar]

My axolotl's water parameters are perfectly fine and the temperature is constant at 66F. However, I keep getting this super annoying hair-like algae everywhere, it mainly clogs up my filter (it might be bacteria growths?). So, when I go to clean the filter, some of it it often falls off and floats around the tank. I am, wondering if that is what this may be, or if it is a fungus.

The algae has gotten caught on his gill before and I blew it off. Is it harmful?
The bit circled in green looks like the fungus, the other pictures has yellow arrows which show the fungus clinging to my axolotl.

I am actually kind of convinced it is not fungus, because it looks like there's less of it than when I looked before.
Just let me know what you think! And how can I get rid of this fungus? Will planting a java fern help?

 

[Caesar]

Update: The fungus part looks almost completely gone

 

[Donna001]

I'm not sure what your problem is, but I would suggest water changes to remove as much of the yuck as possible.
Hopefully one of the more experienced keepers will be able to identify the problem and offer you some advice on how to resolve the issue.