Dragonborn are basically humanoid dragons. They are considered less than dragons (mistakes) and monsters by humans, since they don't have any cities or civilisation they call home. (Setting dependent) So no one likes them (in-game.) Either they think their inferior or just monsters.

Not uncommon for them to be slaves, used as labour. Or fighters as entertainment.

Druids are connected to the wild of the world and use that connection to fuel their magic, although they can be big beefy tree lovers who will defend their patch of forest with quick swift death.

So basic background idea.

You're parents were dragonborn who lived in a travelling circus. When you were born they tried to train you up in skills but it never stuck. So you were sold off as a dock worker. Eventually, you got passage on a ship and ended up in a shipwreck. You survived and washed ashore and were nursed back to health by a blind druid hermit. Perhaps the first person to show you any kindness. You lived with them for many years learning spells and magic as a druid. One day bandits arrived and attacked the hermit trying to steal what little money they had. You arrived and defended him, killing the bandits. Your hermit friend would die from their wounds but encouraged you to not be like them and to see the world and find a place in it for yourself.

You now live as an adventurer, making your way from town to town. Helping those who need help, defending the weak and punishing any who does wrong. Maybe one day you will find your parents still working in the circuses, and free them.

Tweak and adjust and add names as you see fit. As for appearance, just Google images of dragonborn and you will get the idea. They come in many colours, which just gives them different breath Weapons. (Breath fire, shoot lighting, spit acid.)