I also have Disabled Persons Railcard.
The Disabled Railcard is valid the same way in Scotland as it is in England and Wales, so hopefully this is some good news to you.
If you're travelling to Edinburgh by rail, a Plusbus ticket is available. With your railcard this is £2.50 for the day, depending on where exactly you need to get and what modes of transport you'd like to use.
English National Concessionary Travel passes, as the name implies, can't be used in Scotland or Wales. I don't know exactly what type of pass you have but I think we can say with confidence it won't be useful.