Does fire shield damage trigger if cloud rune is used

If a wizard cast fire shield and is later hit by a melee attack, then a fighter uses cloud rune to switch targets. Would the fire shield still do damage?

Fire Shield Whenever a creature within 5 feet of you hits you with a melee attack, the shield erupts with flame. The attacker takes 2d8 fire damage from a warm shield, or 2d8 cold damage from a cold shield.

Cloud Rune When you or a creature you can see within 30 feet of you is hit by an attack roll, you can use your reaction to invoke the rune and choose a different creature within 30 feet of you, other than the attacker. The chosen creature becomes the target of the attack, using the same roll. This magic can transfer the attack’s effects regardless of the attack’s range.