Yes, you are right to use "a hair" as you are referring to a single strand of hair.
If you are referring the entire mass of a substance that grows from the skin of mammals, then you would consider "hair" to be an uncountable mass noun. Example: Hair is made up of a tough protein called keratin.
On the other hand, if you are referring to individual strands of hair, then it can be considered a countable noun.
The hairs on my neck stood on end when I heard disembodied voices emanating from the basement.
Could you help me to pluck the strand of white hair on my head? I know it's there, but I can't see it.
In English, there are things which can be considered as uncountable mass nouns (e.g. nouns describing emotions or substances) or countable nouns if we are using them to refer to multiple entities made up of the same substance or a specific context (e.g. skies, waters)
Some other examples:
Glass (uncountable as a material -- Glass can be transparent or translucent.)
Glasses (countable as spectacles or glass cups -- Waiter, three glasses of water, please.)
Agony (uncountable as an emotion -- The mother who has just lost her son is full of agony.)
Agonies (countable as different episodes that cause agony -- The agonies of war.)
Water (uncountable as a substance -- Water is precious. Conserve it!)
Waters (countable as a region -- Piracy is a thorny problem in Southeast Asian waters.)
Sky (uncountable as the thin atmosphere that surrounds Earth -- Bolts of lightning in the sky are the harbinger of a storm.)
Skies (commonly used in describing the weather based on our observation of the sky -- Clear blue skies are the norm for the southern states in summer.
I hope this explanation clears the air.