Glad you've got the all clear ladylunchalot! And hope your throat clears up. False positives are pretty rare I think (rarer than false negatives at least), so you seem particularly unlucky
I'm hoping they have stocked up on PCRs too for next week. I remember last year the whole world got coughs and colds, and tests shot up in the first couple of weeks of term. Ooor Jason said "don't panic, you don't need to test for cold symptoms" apparently forgetting that often a cough or a fever is a cold symptom...once again, utterly confusing everyone. I think that's about the time I stopped paying attention to what he was saying.
mibbe what a pain for your DS! I do think they should have waited a bit before bringing in the vaccine requirements for travel (without any alternative of testing etc) as it is discriminating against the younger people who haven't been able to get both doses yet, purely due to timing, not willingness. But I suppose, we can't tell Germany what to do! I have no idea about proof, and I'm not sure if there's a formal way of doing it yet, but possibly you could just print out the two different confirmations and throw yourselves on their mercy? (if going to the GP and asking them to amend his Scottish record to show the English vaccine doesn't work? ) It's a bit bonkers, as they are now accepting people vaccinated 100% in other countries, so why the UK is having such difficulty reconciling its nations, I have no idea!