Definitely appeal, a vast percentage are turned down first time. I would if you could get a new letter from doc and counsellor even if it's just reiterating the previous info, perhaps write a letter yourself as well outlining how this condition is affecting you. I know you probably did it all already but it's just the system.
I'm not sure if you can ask for an oral appeal and I know it's a daunting task but in my experience it has the best chance of succeeding as it's too easy reject it when there is no human contact. I know you can for invalidity but not sure about disability. If there is that option I would take it, you can always bring someone with you for support if necessary.
You could also try citizens information office for a bit of advice, you can hit lucky there and get someone well versed in these things, say what it is you want to discuss if you go in so they can guide you to the best person.