As long as you are honest with your use and its purpose, then you have no cause to worry - you have been upfront which is worthy in itself (but I note you have not revealed all you could). If it does lead to you being overlooked for this position, it is unlikely to be subjective or personally directed. Employers look at safety risks to their business and employees, and the position may require a certain requisite for vigilance or some other factors on which this drug may affect performance (even in an office job).
If you are still feeling anxious, perhaps a letter from your prescribing physician may add weight to your argument. Remember, speaking frankly might even be looked upon as a desirable attribute (particularly the stresses of this week) - it is indisputable and the fact that they are delving deeper, suggests you have not been written off, but rather ascertaining if this will be an impediment in your role.