Thank you for getting back to me. I'm glad to hear that she is bright and playful. I think you probably have a couple of things going on here. From the sounds of things I think that she has developed a skin infection. The loss of hair, scratching and licking
, and especially your description of the rash on her stomach
all point in this direction. Skin infections in dogs can either be primary (so just a skin infection) or secondary to something else (usually allergy - which can be to anything - or parasites, for example fleas or mites). Skin problems can be a bit frustrating, as it can take a lot to get to the bottom of them, but if you start from the beginning and work through them you can usually get things sorted out.
What I would want to do for her if I saw her at my clinic was firstly rule out some of the common puppy mites that can happen. These are microscopic little parasites, so you wouldn't be able to see them at home (unlike fleas). It really is a simple test - firstly I would put a strip of tape in her fur and capture a bit of dandruff/flakes, then look at this under the microscope. This would check for a beasty called Cheyletiella. I would then repeat it, but giving her skin a gentle squeeze first to force the other type of mite (demodex) out of its hiding hole in the hair follicles. If she had either of those it could easily lead to a recurring skin infection/shedding problem, and is easily treated by medicated shampoo or an anti-mite spray (depending on what was found, if anything). I would also want to treat the symptoms she has now, so start her on a medicated shampoo (probably allermyl). She may also need some oral antibiotics depending on how her skin is looking.
However, dogs with skin infections do not usually lose their appetite. It may be related if she is uncomfortable which is putting her off, but I would be worried that something else is potentially going on. There are many reasons dogs don't eat, but at her age I would be suspicious that she either had a temperature or felt a bit sick. Either way, puppies don't have much in the way of reserves and can't cope without eating properly for a long period of time. Eventually they can get dehydrated and potentially low blood sugar.
If she just had the skin problem then you would probably be ok getting some over the counter shampoo from your vets to start treatment at home first. However, because she has lost her appetite I think it would be worth making a routine (non-emergency) appointment to get her checked out. The vet would also be able to test and treat her skin as well as investigating why she isn't eating. I don't think it will be anything awful, or serious, but I do think she needs some treatment.
I hope I've helped - if you have any questions from this then just hit 'reply' again and I will get back to you. Otherwise please leave a positive rating.
Thank you, ***** ***** luck, Rosie.