Like you said it will require tests because there are so many diseases that have similar symptoms that it is impossible to pin point a problem without lab diagnosis.
As for the cost, I think your son's life is much more important. I do not see any way of getting $9000 quick enough and a massive nose bleed is no joke because he is loosing blood. If he loses enough fast enough he could end up getting a brain hemorage due to lack of blood to the brain.
Plus there is always the chance that the underlying cause may not require tests because there is a possibility that he may have ruptured an artery high up the nose which only requires a special manoeuvre to block.
When an artery ruptures blood flows out in streams as opposed to a vein which only causes minor bleeding. In any case, forget the money and take your son to an expert.