Hi Snuggles
No you are not obliged to reveal your health details if you rather not engage in what the DWP call the Health Journey. As a carer you should be placed in the No Work Requirements Conditionality Group and not have to attend Jobcentre interviews. If you are worried that the Work Coach does not understand this then you could use the Citizens Advice Help to Claim service and their phone number is on page 2 of the UC Migration Letter.
David
Nothing on this board constitutes legal advice - always consult a professional about specific problems