[Lord of Angmar]

balrogs were fire spirits that sauron bent to his will, whereas he bred the dragons himself.

Balrogs were Maiar that Morgoth corrupted, not Sauron. As for dragons, Morgoth could not create life, only mockeries of it (i.e. orcs). Therefore it must be assumed that dragons had some other origin, but whether they can be classified as "beasts", of the kingdom of thekelvar, has been debated.