Explanation:
We use a comma before a subordinating conjunction that begins a clause that is not essential to the meaning of the sentence. However, when the clause is essential to the meaning of the sentence, no comma is used.
While is a subordinating conjunction. So we need to check if the clause introduced by while is essential to the meaning of the sentence.
In this case, the clause introduced by while is essential to the meaning of the sentence. It tells us when the action in the main clause (I was working) took place. So we do not use a comma before while.
Here are some examples of sentences with while:
I was working while she was sleeping. (No comma is used because the clause introduced by while is essential to the meaning of the sentence.)
She fell asleep while I was working. (No comma is used because the clause introduced by while is essential to the meaning of the sentence.)
I went to the store while I was out running errands. (A comma is used because the clause introduced by while is not essential to the meaning of the sentence.)
I saw her while I was walking home from school. (A comma is used because the clause introduced by while is not essential to the meaning of the sentence.)