My psych teacher said people with anxiety have a sensitive nervous system and are more sensitive to medicine. it seems true for me. is this true?

Not necessarily: I personally have not found that to be true. It depends on medication and circumstance. In some cases, the anxiety disorder has made the person more difficult to treat and has required higher doses of some medications to achieve the desired effect. And I don't know what your psych teacher means by "sensitive nervous system". That term has no real meaning.