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  Hmm, this sounds similar to a case a coworker of mine had with her  yorkie (which had a viral infection in a spot on his skin. Went bald and  bled on the spot). I used to have a male yorkie that every  spring/summer would have flea/grass allergy and it only took one flea to  drive him crazy or being exposed to freshly cut grass, had to put him  on allergy/antibiotics around the times is gets bad. The female I've had  at the time did not have this issue.I work as a hairdresser so granted, my advise is kind of based on human   hair/skin, but from what I've understood they have similar textures to   us so it may not hurt to try ^^. If the fur is a bit brittle and skin  is ichy/dry, it might not be a bad idea to go with something more  moisturizing and definitely fragrance/additive free as you'll want to go  with something that is best for the most sensitive skin. Massaging some  organic coconut oil on the skin/hair (maybe doing it as a deep  conditioning treatment like you would your own hair) and adding it to  foods may also help some, but be sure to keep some kind of healing  ointment on the open wounds and not aggravate it with anything else.  Cleaning it with purified water and a natural astringent can also  minimize the sore over time. A saline rinse isn't a bad idea either to  help with the current sores as it'll provide a more balanced ph and  could help speed healing process. If you have to, you may need to put a  cone on them to keep them from biting themselves (unless that's not the  case).
 There's several factor in a nutshell that I can think of that may be a  probable causes. As mentioned, an allergy or infection (could be  allergic to the products or something else, try the elimination  process), the other may be not rinsing the shampoo enough (residues can  cause bacterial infections or skin irritations) or not leaving in enough  conditioner (taking out too much can leave the skin/hair just as drying  as if you didn't put any on). Another factor is sensitivity, which can  mean that they are not necessarily allergic, but perhaps the ph of the  shampoo/conditioner isn't optimal for this yorkie or perhaps even the water used itself is culprit (I've seen clients who moved to where I live, from another state, comment on how their hair has changed and sometimes it's the change in ph/hard/softness of the water). Or the skin is not  producing enough oil on it's own, thus the dryness and since you seem to  be doing things pretty decently by adding supplements the only thing I  can suggest is what the vet says is not bathing them too frequently. The  average bathing we've done for our previous yorkies was no more than  1-2 a month, give or take if they get stinky/dirty faster ^^ Hopefully  some of this helps or gives you some ideas.
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