Translation:Am I a Klingon? No. You are a Terran.
I would suggest thinking of tlhIngan, tera'ngan etc. as nouns only, not as adjectives, and translating them as "a Klingon" etc.
Like English nouns, Klingon nouns can be used as modifiers -- for example, a tlhIngan SuvwI' is a "Klingon warrior", i.e. a warrior who is Klingon, and tlhIngan Hol is "the Klingon language", i.e. the language of the Klingons.
But I don't think you could talk about, say, tera'ngan bIQtIqmey "Terran rivers" -- because the rivers do not belong to Terrans (the people) but rather to Terra (the planet).
So I think that translating tlhIngan jIH as "I am Klingon" is at least potentially confusing, and I'd recommend against it.