We have a close friend who used to post here,who suffers from a Mental Health problem (depression) so I may be able to help you a little.
Scientists in the US have discovered that "workaholics" produce too much andrenalin.When the body cannot switch off (even for a short period|)the adrenalin production,it just shuts down ALL systems;which produces the depression.
I notice that you seem to have a great need to get back to work,even despite the fact that you (I hope) realise that you are not well?
This is a symptom of the above.
It is often very difficult when you are dpressed to realise exactly just HOW ill you are.Because it is the mind that is ill, and the mind controls our functions,it is easy to brush this depression off,and say if I can go back to wotk I can beat it!
Believe me if you think that way you are wrong.
Try and "work off" depression and it will only get worse.
Your mind needs " time out" now,and the two best ways are to relieve it of pressure(work) and to take medication to help you get over(in a temprary way) the feelings that you have now.
You won't be on medication forever,but you need it now,you cannot do it alone.
Your GP was right to compare it to a physical illness,if you had one you would take all necessary steps to help/cure it,it's just the same with Mental Health.
Everyone can get Mental Health problems,just because you are a qualified person doesn't mean you won't,in fact as I said before someone with a pressurised job is more likely to.
I cannot see your skills going away if you are off work,these skills are part of you,neither the medication nor the mental health problem can take them away.