I think your doctor is right. If she has been doing well in school, she's not ADHD.
Behavioral issues (and even physical ones) are not always resolved with drugs. Look at your family dynamic, and see if she might be feeling troubled by something. (This doesn't mean you are a bad parent! It just means that raising children is hard and complex, and it's normal to have to work at guiding all of your children through the intricacies of growing up. They see things so differently from adults, and can be troubled by things we might never notice unless we really sharpen our perceptions in order to figure it out.)
But it might be a lot simpler than you think...
For one, stress is an enormous influence on concentration. Your daughter might also just have different needs for concentrating. She might need a quieter environment than the others require, or to take more frequent breaks, otherwise starting to feel restless in the middle of doing her homework, etc. This by no means implies ADHD. It can also explain her outbursts - that she has pent-up energy and would benefit from regular exercise.
Also, being the oldest, she started out in a quieter environment. She might just be a sensitive kid and the introduction of three new members of the family in a relatively short amount of time has been a little much for her. Counseling would be very effective in dealing with this and any number of other issues that might be going on.
T.v., too, can be a very disruptive influence on a family, especially on children. The process of t.v. watching, far more than the content, robs families of valuable opportunities for conflicts to arise - because everyone's just watching together rather than really interacting - and to learn how to handle those conflicts. Eventually, without much practice, children don't know how to handle their feelings, which overwhelm them. You might want to try shutting the t.v. off and replacing it with board games, reading times, playing outside, etc. and see if, over time, you can help her address her issues by teaching her skills for communicating what is bothering her.
It is important to play detective for your children, to see what might be causing their emotional upsets. It's so easy just to medicate unpleasant feelings away, but can be so very harmful to them and the rest of the family as a result. So try some counseling, either one-on-one for her, or for the whole family.
Good luck.
L.