Here's another option: When you have very firm beliefs, they are called "convictions" (nothing to do with criminal convictions). I interpret "I'm a very convicted person" as a person with strong beliefs (convictions).

"I'm a very convicted person" -- "I really believe in what I'm doing" "I'm very passionate about my cause"

nozturk, 4. convict (v) to cause a person to acknowledge his error or sin. The Holy Spirit convicted us in our sins. I am a very convicted person. = I am a person who is conscious of and repentant for my sins.

i guess you mean ''convincing'' meaning to speak in a persuading manner . ''convicted'' is used in a totally different context for example ''the thief was caught breaking in and convicted of robbery''