I'm so sorry this happened, your girl was precious and its obvious you wanted to do right by her.
Blaming yourself is natural but its just part of the grief. Don't let it discourage you or make you afraid.
I learned after the passing of my girl that these experiences can make you stronger as an owner. Their health changes and inevitable passing (be it old age or acute illness) is part of the journey when we own a pet, expected or not. Its their journey that we must support them with in whatever way it presents, and its not always easy, clear or gentle.
You were there and you did what you could just as a loving beardie owner should. Its hard, painful, and makes us doubt ourselves but it's something we endure for them out of love.
My heart is with you and your girl, as someone who is still grieving the loss of my own I know how tough it is. :sad:
I would certainly follow this up with the vet, so they know not to put off a beardie with a cough again.