Unfortunately anyone (professional or not) can only self-certify for 7 days, after that a doctors note is reqd.
And our company has certainly got its panties in a twist with absence management in the last few years. I'm sure the AME would have written one had I seen them - but I saw the GP (who prescribed the drugs) and telephoned the AME. So the diagnosis/treatment is by my local GP - the advice regarding the CAA comes verbally from the AME.
Presumably I just ask the GP to state what they have done. It is an airline so I would have thought they would understand. Will prob just get the GP to add - 'on advice of patient/AME' or similar wrt to the 14 day thing...