Sword Princess Amaltea Vol. 2 (manga)

After — reluctantly — following the Queen's orders to embark on her solo coming of age journey, battling a dragon, liberating the beautiful Prince Ossian and getting attacked by bandits, Princess Amaltea is beginning to see that maybe the world isn't as simple as she once thought.

Now she and her rescued prince have a long journey ahead of them, and if they want to get far it'll take cooperation. But with Amaltea too stubborn and arrogant to listen to her fellow traveler, perhaps she'll need to spend a day in his shoes…