Hedgehog
I've no real good advice that hasn't already been covered by others above, but as a sufferer of EDS & mother to a DD who also lives with it, I really feel your very palpable exhaustion, you & you MUST stay strong & deal with this ASAP for all your sakes.
Your GP is disgusting, you definitely need a change, or at very least put in writing to the practice manager what has happened so far & the big mistakes your GP has made in assessment of your DD
I did this when a GP misdiagnosed my own DDs pneumonia several times, patting me on the head like I was a fussy neurotic kid
- I wrote that I was not looking to sue the GP, though I know that was a possibility, but that I just wanted him to learn from his mistake & not dismiss mothers instinct as hysterics again as he did with me.
This resulted in a completely different attitude from this GP, he knew I could have taken him to the cleaners, but didn't & from then onwards he did his job properly, so this might be worth a try.
Also something stood out for me in your post - your DS having scarlet fever & he's become worse since then ??
With my own DD her symptoms became far more obvious after pneumonia - we didn't know what it was back then, they were talking about juvenile M.E. or Fibromyalgia, as I wasn't diagnosed with EDS back then either.
I now know from a long appointment with a specialist at a Londin clinic, that DD also has POTs, this is as you no doubt know, in the remit of EDS symptoms, but was dormant & triggered by the trauma of Pneumonia.
So it could well be you are right & it's a comfort thing & he's feeling his EDS symptoms more, but you still need to stop the BF for all your sakes, his too.
As for allergies - don't rule this out - my own DD is now nearly 12, diagnosed with EDS at just turned 10 - skin & gastro issues since tiny, worse after pneumonia - we knew she was intolerant to chemical food additives from severe colic & raging eczema when she was tiny, but despite an IBS diagnosis at 7 & various gastro specialist, yet her allergies to dairy & soy were never picked up, even though I asked several times as I knew she reacted to harder to digest lactose & wheat when her IBS flared up.
Roll forward a few years & we've recently had her rushed into hospital with severe stomach pain, which turned out to be a classic EDS intestinal blockage - & allergic colitis - her years if IBS related diaorreah was actually her bodies way of dealing with this blockage, which the new gastro reckoned was years old.
We've now got her on a dairy & soy free diet & I've noticed when she's accidentally eaten soy (it's in everything flour related & more & caught us out in a white bread roll) her stomach blows up & she is in pain again
She has almond milk as it's the best for natural calcium & the one she likes most. She also loves coconut milk mixed with cocoa & maple syrup as a chocolate milkshake - maybe this is something you could use to wean your DS off "booby"
Good luck