Does my tang have parasites

[gregzz4]

DO NOT start overfeeding your tank until you know what is going on. If it's water quality related, overfeeding could make it worse.
I realise you recently acquired this fish so it probably has nothing to do with your water quality, but don't pollute your tank just yet.

I see the trailing bits you are talking about and agree it's definately not anything bacterial/viral.
Looks more like some kind of anchor worm or parasitic isopod.
If you can, I'd suggest you try to remove one with tweezers for inspection with a magnifying glass or microscope.
Sure you'll stress the fish, but I'd be concerned about getting it under control as soon as possible.