OK, thanks for the additional info.
If she does have a low thyroid then it may take several months of thyroid medication before we start to see some hair regrowth. So, hopefully we start to see some improvement in a couple of months. It is important to follow up on bloodwork when your vet suggests to make sure that she is getting the right amount of thyroid hormone.
Another thing that can cause skin issues like this is Cushing's disease. However, these dogs usually have the symptoms of increased thirst, urination and appetite.
The "black skin disease" that your vet is describing is also called "alopecia x". It can happen in poms. You may know a lot about it already, but here is some excellent information that may help you:
I hope this information helps! If you have more questions regarding this problem, just hit reply. If I am online I will respond right away. Otherwise I will respond as soon as I come online again. Or, if my answer is sufficient, then please hit accept. Thanks!
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.