I think you were understood.
used to express polite or formal apology or regret. "I'm afraid I
don't understand" synonyms: sorry, sad, distressed, regretful,
apologetic "I'm afraid that your daughter is ill"
However, I'm afraid you used it incorrectly. In answer to your father, you are probably not apologetic about not wanting to be a doctor.
"I don't wish to be a doctor as I am not interested in medicine."
"I don't have the time or inclination to study that hard."
You might literally be afraid that you won't measure up -- that you are not smart enough to be a doctor.