Hi Tina
I am not sure what you are asking, you say that you won an appeal for LCW but then go on to say your UC has been closed.
As to the second paragraph in your post, if you were to start a new claim for UC, I would assume that you will have to make a new claim for LCW. I don't see what effect your son claiming carers allowance for you would have on your claim.
www.gov.uk/carers-allowance You need to get advice from your local Welfare Rights Organisation;
advicelocal.uk they will be able to take all your circunstances into consideration.
Gary