Warforged Toad With Heat Metal

In 5e, if I'm playing a Circle of the Moon warforged druid, and my bard friend casts Heat Metal on me, do I retain that effect after wild shaping into a Giant Toad? (I want to be able to use a bonus action to deal 2d8 fire damage to the swallowed and bitten creatures.)

If I was wearing armor using Integrated Protection and that was the target of the spell would that work?

Yeah if someone wanted to pull this off I'd argue that they can do it, but they'd be taking the damage every round it wa active as well.