Have you discussed the idea of OCD with your doctor? It's very common for people with ADD to ruminate. If the rumination is only from the ADD than the medication will probably help. If you do have a co-existing anxiety disorder like OCD that will also need to be treat in order to stop the obsessive nagative thinking.
Comminication with you doctor is key!
I agree that the negative thoughts can be related to the ADD. It is part of the overfocus or trouble shifting out of a 'rut' that goes along with some types of ADD. I tend to do this very easily.
I read somewhere too that this latching on to negative thoughts is the brains way of trying to anchor all the scattered thoughts flying thru our heads. The negative thoughts have alot of emotional impact so they successfully 'pull us in' to anchor us even though its on something hurtful or destructive. The pain of that is better as far as the brain is concerned than the scattered thoughts.
Medication should help. If the medication you are on doesn't than you may need to try different doses or meds. Please make sure your doctor knows you are struggling with this. Its not anything you should feel ashamed or badly about -- its really just part of the ADD.
Another possibility is depression aggrevated by ADD. Again something that has to do with brain chemistry and can be successfully treated.