DA
You need to get face to face advice from your local CAB and/or Welfare Rights office.
It is possible that the DWP will accept you and your carer are not partners, however, it is also possible that they will not, which is why you need to seek advice.
Do you have a rent book or at the very least a formal arrangement for the room(s) you occupy in their house? Is the house segmented in any way, for example, do you have your own living area? Without these it may be difficult to prove to the DWP that you are not partners.
Where to get advice? Good luck
Gordon