Applying to more selective programs after having been diagnosed with a long-term mental condition
It's certainly a huge relief to finally know, after years or decades of struggling, what the underlying problem is. But people with ADHD tend to assume that a diagnosis and treatment is a magic bullet that will suddenly make them like everyone else. I think part of this is ADHD tendencies and part is internalizing the erroneous belief that if you just tried harder you'd stop screwing up. I don't have any first-hand experience with ASD, but the issues seem to be similar. 

So here's my first observation: A diagnosis does not "fix" ADHD. A diagnosis together with medication and therapy or coaching does not "fix" ADHD. Right now you're at the starting point and you've been pointed in the right direction, but it's probably going to take some time and experimentation to find out exactly what you need to successfully manage advanced academic work. Expect that what you need might be really different than what is ordinarily offered in an academic setting. Don't beat yourself up trying to be like the neurotypicals the work is designed for. 

My second observation: As you can see from the answers already given, many professors and programs take the attitude that learning disorders/differences are the student's problem and it's not their job to deal with them (except maybe in a very superficial legally-mandated way). This attitude might vary by country--my own experiences in the US have been pretty dismal. So even once you know what you need, and even though the law is on your side, you might find yourself fighting a losing battle against these attitudes to get it. So it's also important to be sure that you're entering an environment that sets you up for success. 

I honestly don't know the answer to this second problem. I might post a related question here later to see what the ASE community thinks. I don't mean to sound pessimistic, but the fact is that the academic community is on the whole not particularly welcoming to people with learning differences, and ADHD is particularly misunderstood. The trick here is to find the exceptions who will provide the conditions you need to flourish.