There is a principle of law called "sovereign immunity" that says you can't sue the government unless the government consents to be sued. I know of no principle of law that would permit you to sue the EEOC. I also seem to recall that the nonissuance of a right-to-sue letter after a certain length of time creates a circumstance where one is deemed to have the right to sue and to have exhausted admiistrative remedies. I don't think one has to have the letter in hand, and one certainly doesn't have to have the EEOC papers in hand to hire a lawyer to file suit against employer to preserve the claim.
Not legal advice, just my two cents. I don't practice law in Louisiana or hold licensure there. If you need legal advice, please consult a lawyer who does.