If you (1) received a withhold of adjudication as to both counts & (2) you successfully completed probation as to all counts without violating probation & having your withholds converted into adjudications, then you were not convicted of those offenses and your answer is completely honest and accurate as to those counts. I assure you they will do a thorough criminal background check and they will be made aware of your complete criminal history, so I suggest you secure a certified copy of the plea & sentence from those charges so that you'll have it at the ready when the discussion of priors begins.
If the crimes were drug related you may have difficulty in applying successfully for a medical residency training as they're apt to look for someone with no drug blemish whatsoever although you can in all honesty state that you have never been convicted because the adjudication of guilt was withheld by the court. You also need to be aware that a background check will reveal not only the arrest, but the fact that you were prosecuted for the crime.
You need to stress that not only were you not convicted but that over the last ten years you've never had any other problems with the law and that the entire experience has taught you many things not just about yourself but about life such as how to handle adversity and make the most of life.