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The spots appearing after bath immediately are suggestive of dried epidermis
layer getting soaked and being visible.
this can happen if you had touched a hot surface but there was no blistering but only singing of outer skin layers.
The keratin layers will go away in some days.
The problem is not of any clinical consequences and heals without treatment in a week by itself.
It is not raynauds because raynaud's should be bilateral and affects all fingers mostly all length and is painful.
I hope the advise would be informative and useful for you.