The quest isn't to find something about the PC's past. The quest is to prevent the PC from ever finding out about their past.
You haven't given much (any) detail about your setting, so there isn't a lot to riff off. So I will riff off elements from my own game, and maybe you can pick something out of it.
Millennia past, when the dragons rose up against their demon overlords, they needed footsoldiers for their fight. However, the lesser races were primitive and of little assistance. In desperation the dragons broke their long taboo of mixing dragon blood with the lesser races and magebred troops, humanoids with draconic toughness and an affinity for magic. With the help of these tainted dragonspawn they won the war, and the fiends were bound uneasily to dungeons beneath the earth. But not before the Overlord Tiamat laid her curse, so that the dragons whose colours matched her own were born with evil in their hearts, and draconic society crumbled.
In the aftermath, the metallic dragons set out to destroy the abominations they had created. But some escaped, of course, and blended with the humanoid rabble, and bred like the vermin they were; or so the dragons viewed it. The dragons tried to root them out when they could, but the mongrels' blood became much diluted over time, and other then the occasional sport with an unusual talent for magic - the odd sorcerer who needed no spellbook - they became too hard to identify and too little threat to be worth the effort.
Or so the dragons thought. But then scholars of the Draconic Prophecy found references to the dragon-blooded in the scribblings of Ourelonastrix. And it became clear that some of these creatures had a role to play in the Prophecy, some of which were a great danger to dragonkind. And so the dragon-blooded became unknowing soldiers in the secret cold war being waged between the metallic dragons and the servants of the overlords, to manipulate the Draconic Prophecy to prevent, or enable, the overlords to be freed from their bindings.
Unbeknownst to the PC, events have occurred in their life that suggest they might be the Dragon-Hearted Prince referred to in prophecy. The answers, and keys to ensuring the Prophecy unfolds in a manner most beneficial to dragons, lie in the Library of Castle Amber. Castle Amber was a stronghold of the dragons during the war; built out of time to protect it from attack, its original guardians still live and would know the ancient stories and be of great assistance in interpreting the Prophecy. But millenia of isolation and the energies of the place have driven the draconic guardians quite out of their minds, and they no longer know who they are or why they are there. They live bound to humanoid form by the fantasies they have created for themselves, forgetting even that they are dragons.
Neither (most of) the metallic dragons nor (most of) the servants of the Overlords want the PC to die; if the PC is indeed the Dragon-Hearted Prince, the seals binding one of the Overlords might be strengthened or weakened, depending on the PC's actions. Rather, they want to manipulate events to the outcome they desire. But the Prophecy resists force, and both sides have learned that they cannot coerce events, but must act indirectly.
And so the agents of Tiamat have manipulated some other party, some grand wizard or lesser divinity, to place a quest upon the hapless PC. That party would have believed they were acting in their own interests, and may have acted directly, but might also have thought they were doing something else; perhaps the quest was placed in a trinket intended for another NPC but lost in a bet to the PC. But in any event the PC has been bound to destroy the Library of Castle Amber, and to slay those guardians who may hold the key to unlocking the Prophecy. Because only the Dragon-Hearted can go the the Forgotten Castle.
To complicate matters, not all metallic dragons think it is worth the risk to keep the Dragon-Hearted alive. And the servants of the Overlords all have their own agendas, some of which may conflict. So there are some factions out there that would be perfectly happy to see the PC dead, if they learned their significance to the Prophecy.
So, uh, yeah. Castle Amber, "Amber family" are polymorphed dragons who have lost their collective minds, modify as needed.