Update:
Back from the vets now-
The vet had a very good feel of Dougie's abdomen and legs, stretching and bending the joints, she says there definitely doesn't seem to be a break or fracture, and that there is no swelling on the leg. She said her tummy looks and feels normal, and since she's laying normally, she is convinced that her problem is purely muscular. She sent us home with an anti-inflammatory pain meds to keep her comfortable, and instructions to continue hydro-therapy as much as possible. She agreed that egg production could be making it more painful for her, but for now the pain medication should help enough. If in 5 days nothing has changed, or if she is still in a lot of pain at night, I'm meant to bring her back for X-rays to double check theres nothing else going on, and perhaps go ahead with the hormone implant to give Dougie some relief. But the good news is she thinks Dougie will be just fine.
I could tell she didnt know everything about ducks (for example, she suggested syringing the pain medicine into her mouth if she wont take it in her food), but she definitely seemed competent handling poultry and seemed knowledgable in other aspects, asking all the right questions etc. So with her help, and this forum's advice combined, I think we'll be okay
I've given her the first dose of medicine, just put it on some peas and she gobbled it down easily.
Everyone at the vets loved her, and the receptionists went crazy over her story of coming from Sainsburys eggs and hatching on Christmas day lol.