Reddish spots referred to as blotches are bacterial and often a sign of poor water quality and diet which triggers a vitamin deficiency
The red blotches look like septicemia, which is bacterial. Unfortunately, it looks like antibiotics are needed here. Quarantine him, and provide heavy filtration and an airstone for added oxygenation. In my experience, most truly effective medications are not reef safe, so quarantine is a generally a must. What has he been eating? Tangs need a lot of greens in their diet, but will usually eat meaty foods, too. If he's reluctant to eat, try opening a live clam, mussel or oyster for him. Be aware that the shellfish will cloud the water temporarily. Normally, I use Kanaplex when I see red spots or blotches like that, and it might apply in this case, as well. The lacking appetite and fin deterioration are of concern, but Kanaplex may be sufficiently broad spectrum to handle all of the symptoms. I have a pearlscale butterflyfish in QT who was showing similar symptoms to your tang, but less advanced. I did a regimen of Kanaplex, followed by General Cure, and he appears to be recovering well. Should his appetite return, you'll want to really push the seaweed, and treat it with Selcon and a vitamin preparation like Zoe. Various herbivore preparations should be offered, as well. Get an algae clip, or rubber band the nori to a rock so he can pick at it all day. Mysis shrimp is also good. Last year I received two pyramid butterflyfish who were in poor condition and not eating. After a few days, I was able to restore their appetites with live copepods. I thought that the copepods were too tiny for the fish to bother with, but they fed very enthusiastically.
