미쳤어 is composed of
미치(다) + 었 + 어
었 is a suffix used to express past tense
어 is a ending particle
미치겠어 is composed of
미치(다) + 겠 + 어
미치다 means "mad"
겠 a suffix used to express one’s opinion/idea/assumption = I think, I guess, I assume
어 is a ending particle
내가 미쳤어 means "I was mad"
내가 미치겠어 means "I think I will be mad"