Skin pigmentation. In my bathing water!

Thanks for your query. I don't see any connection between skin allergy and hair loss as they have different underlying causes. It is unclear from your question whether the diagnosis of skin allergy is made by a Dermatologist or it is your assumption. There are hundred of skin condition which all present with rashes and it needs expert evaluation to reach a diagnosis. Skin allergy leads to hives which usually lasts for less than 24 hours and goes away without any dark spots. If you are getting dark pigmentation after the rash is gone the diagnosis of skin allergy is in doubt. There is a form of skin allergy known as "Urticarial vasculitis" which can lead to pigmentation after rash is improved but this condition is rare and only skin expert can make this diagnosis after skin biopsy.

Please visit a Dermatologist for evaluation and treatment of your condition.

Please avoid self medication as it may cause more harm than good in many situations and causes delay in seeking expert opinion.