Actually, "I am my career", I think…right? Because of the ending on kariyerim indicating the possessive?
In benim karierim "my career", the -m is possessive. (You need a vowel to attach the -m to a noun ending in a consonant, thus karier-i-m. No vowel in, say, şemsiyem = şemsiye-m "my umbrella".)
In ben karierim "I am a career", the -im is the first-person singular verb ending ("am").
For "I am my career", you would need ben (benim) karierimim.