I will start off by saying I do not know what the oddly pigmented patches of skin on your animal may be, and that if the changes have been taking place over a 2 year time span then they may be normal pigment changes, or at least not too pathogenic. But I question if part of the problem may be inappropriate husbandry.
Now that I see the pictures I wonder if the habitat is too dry - the soil looks somewhat packed down with little to no moisture. Tiger salamanders prefer to burrow under the soil, so with that in mind do you think your soil is loose, deep and moist enough to allow that?
My tiger salamander is kept in a large Rubbermaid (about 3 feet long and 18 inches wide) on a mix of damp coco fiber and organic potting mix about 6 inches deep. I keep the soil mix damp enough that I can form a ball out of it, but not dripping water when it is squeezed. I also try and do a moisture gradient, meaning that when I add water to the soil, I only add to one end. That way, one end is more moist than the other and the animal can choose for itself where it would like to be. I keep cork bark hides as well, but mostly the salamander burrows pretty deep into the bedding and doesn't mess with the hides at all. And to be honest, a lot of the time I don't keep a water bowl in with mine - I often forget or procrastinate putting the water dish back in after cleaning it, and I bet its the majority of the time that there is no bowl in the habitat. But I feel that since in the wild a tiger salamander pretty much just goes to water to breed and the rest of the time is hiding under ground, and as long as the substrate is the appropriate moisture level, a water bowl is not crucial.
If you feel that the skin changes occurring on your animal are effecting its health then do not hesitate to seek veterinary care. However, in addition to that some housing modifications may be in order.
Good luck!
HJ
