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Seven weeks is usually considered too young to have food allergies.
If it was just the ears itching I would think ear mites but since it's other parts of the body also, I would think other types of mites (sarcoptic or demodectic). Has she had a skin scraping?
Six weeks is really too young for her to be away from her mother, so she will have to be watched extra close for hypoglycemia. Because she had a vaccine so young it would have counteracted the immunity that her mother gave her making the vaccine and the immunity from her mother "ineffective", so she is totally unprotected from disease right now. This happens to most pups but because she is so young, I would hesitate letting her walk outside at all.
It's hard to say where the cough came from.
What was in the vanguard vaccine?