You could apply as a start but know that you will most likely be in for a battle. My mother had gotten disbability benefits due to her having schizophrenia but she was denied at first despite the fact that she had already faced a lifelong struggle with her mental illness and was unable to work. We had to appeal and provide much proof of her disability.
It will probably need to be shown that you have taken medication and despite these efforts you are still unable to work. You definitely need letters from your doctor(s).
My son receieves benefits but he has extreme autism. Again we had much proof and documentation to clearly show that my son has a disability which affects every aspect of his life.
So just know that this will most likely be a very difficult battle for you and the money you may receive is very little.
Here is an article about this topic from ADDitude magazine.
And it seems even getting accomodations at a job for ADHD is very difficult according to this article: "In other words, if a child, teen, or adult with ADHD can "get the task done" or "get the job done" by using medications, applying behavioral management techniques, receiving counseling, using biofeedback, using Attend, or other treatment interventions, then they do not have a disability that is protected under the ADA."
Here is another article about how difficult it can be to gain benefits for a child with ADHD.
If you are still undaunted here is the social security disability web site for beginning the process. And here is their number: 1-800-772-1213
Hope this helps some...let us know what happens. Good luck to you!