Perhaps easier is: "Asking me to explain issues she came across in her studies, my sister always told me that I am a teacher by nature." Were you practicing the subjunctive case? Personally, I avoid this altogether, as it sounds like a grammar book. However, I do think that you succeeded. PS: "I am" is better, as it what you are, or part of your personality, nature.

Is it correct to say 'I am a teacher' or 'I was a teacher'

This looks good Mohamed. Is your aim to practice using the modal 'would'? If it is, then good job, there are no mistakes!