Tribunal win and esa

Scissors

Evening all new poster here. I recently won my esa appeal and dwp dot appear to have received confirmation from the courts despite it being sent by email on the day and also hard copy handed to dwp representative. Five weeks on I had the courts email another copy over to dwp which they have not received. Was told to take my forms to jc and have scanned over they refused as I didn't have the correct address to send it to so phoned again only to be given a different address to the first one. Return trip to jc and they finally accepted the address and scanned my paperwork.
Dwp said they are sorry and it should have been sorted within a week.
Anyway sorry about the waffling, what I want to know is will dwp use any back payment for tc overpayment. Or as I was entitled to the money before they stopped it can I request that they pay me. I already in a payment plan for tc.
I need to purchase some disability aids and white goods which are needed due to my problems.... I was buying theses on pay weekly but had to return as couldn't afford repayments after dwp failed my esa assessment.
Any advise would be much appreciated. Thanks