Nick
Is there anybody else that can go with you to the medical?
I think it is a good idea for your sister to write the letter you refer to, ask her to also explain why she is writing it, e.g. that you have difficulties conversing with people
It would be worth you sending a copy of your GPs and your sister letters, direct to the DWP for the attention of the Decision Maker.
Good luck with the medical
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems