Yes, ADHD is Hereditary. However, it is not unusual for only one child in a family to have it. Or to even skip a generation or for neither parents to have it, but an Uncle, etc.
Point, being - your child might or might not have it. However, if your child has it - it does not condemn him/her to going through what you went through. Chances are your parents had no clue what ADHD was and that effected how you were treated. And I certainly know that the medical profession has come a long way since you were diagnosed. However, it does kind of depend of the type of medical help you get.
The main thing to remember is that YOU are the main advocate for your child. The more you know about ADHD, the more you can help your child. Even the medications are much more improved then when you started them. I have a ton of information that I can send you any time you need it. But, I would say for now, Relax and enjoy!
If you're concerned that a doctor will simply say your child has ADD/ADHD and you feel he/she might be wrong, there is an actual test for ADD/ADHD that is extremely effective. It's called a qEEG, which is similar to an Electroencephalography (EEG) that measures brain activity on the scalp. The qEEG differs from a normal EEG because it compiles the measured data and provides a result that shows whether or not someone has ADD/ADHD. It's not 100% accurate, but it has shown to be 96% accurate in defining people without ADD/ADHD and 86% accurate in those with ADD/ADHD.
Some, or even many providers might not offer this test and insurance might not cover it, but if you're looking for peace of mind, it might not be a bad route to take.