Yes, that’s how options exercises work.
> They are now worth millions of dollars on the open market, but the company will not allow me to sell them...
But you were prrsumably aware of that limitation when you entered into the agreement under which you purchased them (if you dispute that that is the agreement you agreed to, thebmn, definitely, you need a lawyer.) So, even insofar as you describe the “open market” accurately, that market isn’t open to you.
> I understand it's risky, but at this point they just aren't letting me get a payday...
Perhaps not. Are they obligated to let you get a payday? Is it in their interests to do so? If neither of those is the case, why do you expect they would?