Chattie sez: The correct phrase is “got my goat”. This idiom means to annoy or anger someone1. It’s often used to express irritation or frustration with a situation or individual.

The phrase “got my goad” is a common misinterpretation and doesn’t have a recognized meaning in English3. The word “goad” is a verb meaning to provoke or annoy someone in order to elicit a reaction3. However, it’s not typically used in the phrase "got my goad".

So, if something is bothering or annoying you, you would say it “got my goat”. If you are trying to provoke or stimulate someone into action, you would be "goad"ing them.