Learn English – ny difference between” yet ” and “and yet”

Because is a subordinating conjunction, which means it introduces a new subordinate clause. Your example

The reason she’s so irritable is because she’s tired.

Is correct

Because of is prepositional. It needs a direct object, not a that-clause

The reason she’s so irritable is because of her work.

Is correct.

P.S: For me, the usage of "because" is redundant here. You have "The reason" in front of your sentence, so introducing the reason with "because.." is not necessary.

A comma after a coordinating conjunction (and, or, but) is only acceptable when the comma is the first of a pair of commas bracketing a ‘supplement’—a phrase or clause which lies outside the main structure of the sentence and interrupts the flow of thought.

  And, as if that were not enough, he went on to sneer at the victim.
     ^---------------------------^  

  But, as you said, there is no point in trying too hard.
     ^------------^

In other circumstances the comma is effectively ‘disjunctive’ and subverts the joining effect of the conjunction.

This counterproductive comma is becoming very common in contemporary business writing; I suspect it represents a hypercorrection by people who have misunderstood the need for commas bracketing supplements, or think it lends formal ‘elegance’ to their writing.