My son is somewhat prone to nosebleeds and gets them several times a month...and every night for a couple of weeks when the seasons change.
Honestly, I think you're making a mountain out of a mole hill where nose bleeds are concerned. If you think he has blood clots in his brain, ask for a CAT scan... but if he had clots in his brain, he'd be doing a lot worse than nose bleeds... and he wouldn't have lasted 2 years untreated.
Clotting is the opposite of bleeding. The fact that he has clots coming out of his nose, is an indication that his body is trying to stop the bleed... and he blew the clot out. It doesn't mean there's a clot in his brain that somehow fell out his nose. really.
You say he gets the nose bleeds when he takes Claritin. That's an allergy medicine and LOTS of people, especially kids, get nose bleeds when their allergies flare up. I'd think it was the allergies (that made you give the medicine) that caused the nose bleeds rather than the medicine causing them... but hey... why not stop giving him Claritin.
Similarly, kids get fevers when they have a virus. If he's prone to nosebleeds, he may also get nose bleeds when he's sick... so the fever and nosebleed are both part of being sick, but the bleed didn't cause the fever.
I hope you get to the bottom of this, but I also hope you don't subject your child to needless procedures because you won't accept the analysis of (now 3) doctors that this is inconvenient but normal.
If he's really hitting his head that hard every time he plays THAT is what you should be concerned about!