"I am sincere." "My love for you is genuine." "I am honest. I don't lie." "I am faithful. I don't cheat." "I am loyal. I don't betray my friends." "I am genuine. I am not hypocritical." There are many ways of describing good personal qualities. There are many adjectives other than "true".

"I am authentic." "I am true" could be puzzling. To say that a PERSON is "true" often means "faithful in love."

In the context that you want to use that phrase, many native speakers say "I'm real!" I suppose you could consider it a bit of a slang.

You can say I'm true but you can't end the sentence like that. If you say I'm true to myself it's correct.

I'm real.