She is still young but you could take her to an OT (Occupational Therapist) and mention your concerns. They will be able to tell you if her behaviour is age appropriate or needs attention.
I think you will need a referral from your GP to see an OT. My DD was referred by a nurse from a child health clinic when she was 18 months. Just tell your doctor you have some concerns about her behaviour and would like a second opinion.
When they go to the OT they basically just play with the child a bit and watch their reactions and ask you a bunch of questions. They will also make some suggestions about what you can do to help her if they feel her behaviour is developmentally innapropriate. I don't know about testing specifically for ADHD at 3 years. If further testing is needed they will direct you how to go about it. My DD tested below the norm for attention span - the OT offered me advice on how to improve it and then told me to return when she is older if I was still concerned.
I understand your concerns - I have read some of your other posts and your DD and mine sound very similar. I share your frustrations. People have been asking me if my DD has ADHD since she was 12 months old yet all the professionals have told me a million times she is normal (which I also believe - I prefer to think of her as strong willed and high spirited).