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The reason in your case which I feel is fungal infection
.This is because fungal infection can occur after salon work and it can also detach the nail.One thing which we also see is nail discoloration .The nail wont grow back on its own if the fungal infection is not treated effectively.
The best advice would be to consult a dermatologist
and get a KOH examination done from your nail .This is to detect if there is any fungus.If yes,then you need a oral anti fungal medicine along with topical nail lacquer.This nearly a 6 months treatment .
Once treated completely the nail would grow back good.
Hope I've answered your question.