Hi , I had to appeal my first award when, like you, I got no mobility despite the visiting DLA doctor knowing that I had mobility problems.

I wrote a really strong letter stating my case and saying I was not mobile like they assumed I was. They then awarded me higher rate mobility - so work that one out

I said nothing in the letter that had not been said on the form, I don't think they read the supporting page properly.
But it kept having to be renewed every two years, which if you want a Motability car is useless as you need three or more years at a time to qualify. So after receiving the two years award for the second time I wrote what still reads like a very very angry letter, explaining that lupus was for life, that told them exactly how the pain affected my life and trapped me at home etc etc. and that the stress of constantly having to apply was not a good idea for seriously ill people, I expected it to be ignored but within four weeks got DLA awarded unconditionally.
The forms were originally filled in with an expert community nurse and she could not work out why they only awarded after follow up letters/appeals. She told me to fill the forms in as if absolutely the worst day was what every day is like.
But do get expert help/support if you can. A friend got help from Citizens Advice and they sorted out other unemployment type benefits and support for her as she lives alone.
Good luck. It is a horrible process having to almost "beg" for something you are entitled to but keep at it and you will feel a lot better in the end. I was on a similar support list when I was doing my application, it kept my morale up and kept me going.
Kind wishes
Sara