With regards to drug screening: when you get a drug screen, you fill out a form beforehand telling them what medications you take, and sometimes they will request to see a copy of your prescription if it is something that can be abused. Friends I have had who take a modest dose of Adderall have actually not turned the amphetamine portion of the drug screen positive when we have taken these tests at one of our rotation sites.
The offices that do these screens are sometimes completely independently contracted, but at the very least are completely separate from anybody you will be working with in the clinical setting -- they provide the rotation site/department with a "pass" or "fail" result. A positive test with a prescription that accounts for it would be reported as a "pass" although at some places you could be required to undergo a quantitative or more specific screening before they would give the "pass" (I would hypothesize that some places could want a note from a physician in addition to seeing the rx).
So many people in medicine are legitimately on Adderall that even if your instructors knew, they probably wouldn't care. I have trouble envisioning the scenario in which they would find out short of you taking your meds in front of them. (as has been mentioned above this is not something to put in your app either).
Completely independent of any commentary on your need for the medication etc., I am disturbed and disappointed that a physician would give such an uninformed and incorrect piece of advice to you. Worse than any stigma of taking Adderall is the stigma of failing a course, year, or rotation, the financial consequence of having to repeat a year, or being hurt in the match by such a blemish on your academic record.