here is another possibility sebaceous adentitis and this is tied to thyroid issues so why you need to have thyroid checked out with any hairloss and this can only be diagnosed by a punch biopsy
Sebaceous Adenitis
if it is this there is a group on yahoo for this but what they do is oil baths so they soak the dog in oil - mineral oil, coconut oil, and some use baby oil which i would not use then they bath the dog after the soak of 20-30 minutes - dr dodds recommended to me murphy's oil soap it is pure vegetable oil so i bathed dd in it as she is hypothyroid and sebaceous gland excretion and you combat oil with oil - usually with sebaceous adentitis vs sebaceous gland excretion they are dry skin vs oily skin but some use the murphy's oil soap with sa and have had great success with it . I freaked out called the mfg and they said many people use this with kids with eczema and psoriasis i bit the bullet and washed dd in it - her coat looked amazine all crusties gone but it has citronella in it which is great as a flea protection too

but she was itchy from citronella so this is something you may want to try as it will not dry out the skin
usually to join that yahoo group they want you to have done a punch biopsy to determine if it is SA first
see it is tough as without culture, thyroid panel, and punch biopsy and dermatologist exam it can be a few things
it can even be just environmental allergies but having a dog with env allergies she does not have that skin looking like that so i think it could be more than just Env allergies
she will save alot of money and aggravation going to a dermatologist - they charge about $160 for first consult and $87 for follow ups but you will get the answers you need
what food is your mom feeding?
and also skin conditions are usually due to auto immune diseases which runs very heavily in this breed and due to inbreeding this line which is what this lady guaranteed was doing and why this baby suffered and i am sure the lady is continuing to do it so other unsuspected pet owners will end up with these dogs like i did which makes me so ANGRY as it has been a nightmare for 5 years with my allergy dog and i have spent 8k trying everything to keep her comfortable and she is an akc yorkie - NOT COOL. These health issues on allergies and skin do not show up until the dogs are about 6 mos to 3 years then you are attached
sadly these dogs end up in rescues and abused as owners get frustrated as it is hard to see a dog itch and be uncomfortable or they end up on heavy doses of prednisone causing other health issues. There is no cure alot of time for allergies unless food but not for environmental so i am hoping this baby just has a condition that can be treated but you need to get a firm diagnosis and you will only get that with a dermatologist not a regular vet