I can't believe your pdoc won't write you a medical exemption note! Now THAT is crazy.
I would absolutely go back to your original pdoc so you can get that note.
And I relate to the embarrassment about going back to work. I worked part time and then was given a big promotion to full time last year. Unfortunately, that coincided with my severe manic episode and I wound up hospitalized twice in the first month of the job. Long story short, I told them that I had a medical issue that was making it impossible for me to work full time. I also explained that the odd behavior (I had hit the severe black of depression post hospitalization) was due to my medical issues. They allowed me to take a month and a half or so off and then I was able to return to my former part time position, which is what I'm doing now.
I had sooooo much anxiety around quitting the full time gig and asking for my part time position back, but it ended up working out perfectly. Sometimes the worry is worse than the actual event. I would figure out ahead of time what I wanted to say and then give your boss a call. I personally did not want to disclose my MH diagnosis so I made up that I was in the hospital for colitis and suffered from Crohn's disease. It worked like a charm and they were very understanding. HR never likes asking questions about medical issues so they won't pry (I live in the US but I imagine it's similar to where you are).
So yeah, first things first is get that note from your doctor. You can ask him to write it however you want to, my note didn't say any diagnosis.
As soon as you get that in place your golden. Even if your performance wasn't great in the past, once your boss knows that you were sick it's not such a big deal. People are generally understanding and you don't have to go into detail. I actually rehearsed the conversation with my mom prior to talking to my boss! My mom is actually a nurse administrator and hires people all the time so she knows all the ins and outs of this sort of thing, and she was the one that suggested the approach.