Well, there is no way to know if it is an ADHD problem based on just what you have said. And its pretty hard to get it diagnosed at 3 anyway. Sleep apnea is definitely worth looking into. But if she really is going all day long from 7 in the morning till 11 at night - wow, she is getting way less then the recommended hours of sleep. I think the idea of lots of physical activity as suggested by both 0f the above is important. And just as important is the calming night time routine the specialmom mentioned.
When you say she is,"still be up 11pm with alot of energy." I am assuming that you have tried to put her to bed and she keeps getting back up. Or you just what? As specialmom asked, what is your night time routine? It may - or may not -be part of the problem.
This is not an ADD/ADHD problem. Not getting enough sleep at night can make you hyper during the day. The first thing to check for is sleep apnea. Look in on her when she is sleeping. Is she mouth breathing and/or snuffly? If that is not a problem analyze her diet. Sweet cereals, bottled juices, sodas, desserts, candy. These treats should be held to a minimum because sugar makes children hyper (and tired).
If sleep and diet check out, consider that you may simply have a very active child. Such a won should be provided with lots of physical activity.
What kinds of things do you do during the day to 'wear her out'??? I have energetic ones too and that was my daily mission. As much physical activity as possible to slow that engine down. We swim, run around, go to parks, etc. for as long as possible every day. It does help.
we also have a calming night time routine. how is your night time bed time routine?