Let's start with your incorrect premise: an Area of Effect does not go around corners (unless specified by the effect). There must be a clear path to the point of origin for the effect, and then a clear path from the point of origin to the affected creature. This might seem like going around corners but is actually two straight lines. [See Area of Effect and Cover, DMG p251.]
In the case of dragon's breath, the point of origin is the dragon, with the Area of Effect being a ray or cone. Thus, there must be a clear line from the dragon to the target.
Arrow slits provide 3/4 cover [DMG p251]. Dragon's breath would come through the slits. If there are places on the wall where you could stand away from the arrow slits, those spots would have total cover (see below diagram for a cone AoE).

Thus, if you are standing at the arrow slit casting spells or shooting at the dragon when it uses its breath weapon, you would need to make the required save.
By RAW, 3/4 cover gives +5 to AC and Dex saving throws [PHB p196]; however, a DM may house rule advantage instead of +5 on the save if a square with total cover is next to you.