ok just got back from derm and she said the nose is not from zinc as zinc deficient dogs have crusty nose and it runs in huskies and malamutes not yorkies. She said for dd it is either due to staph infection affecting that area or she strongly feels dd thyroid has gone down and it is her hypothyroid and she needs her meds adjusted since she is having hair loss all over

So i would strongly recommend having a thyroid panel done if none has been done to rule this out. She said if it is not either of these then it is due to steroid use as well as dogs can have loss of hair due to steroid use.
just wanted to pass this on in case it can help