Hi Havana
Only you can decide what to do here. It certainly shouldn't be held against you, and nor do you have to discuss what led to your addiction. Your health professional has expressed concern and wants to put it in their letter. You don't have to submit the letter, but if you don't and they are right about the possible impact on you from the pressure to work - all the work you have done to get to where you are now could be undone. People cannot help if they are not aware of what has happened.
But this is your choice and only you can decide. You have to do what feels right for you.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems