First of all, you're not doing anything wrong and everything is going to be okay. Traumatic Brain Injury affects everything about our hardwiring - and depending on where the injury was, the extent of the damage, etc., it can affect a LOT of her life.
My mom had traumatic brain injury as an adult and she had to relearn everything. Her moods and behaviors ran the spectrum and for a great deal of time she could not control her emotions. I can't imagine what that might have been like for a middle aged woman to experience!
The good news is that your daughter is just a small kiddo, and at the age of 5, she has plenty of time to keep wiring and re-wiring her neural networks. See, if the brain runs into a serious roadblock such as damages, it will figure out a way around the roadblock and figure out how to keep on going. Just remember it will take time. She's very young and has a big hurdle. But she's young and she'll learn her way around it and become a successful woman :D
And honestly, no i don't think she should be on medication as a child. I STILL have trouble focusing, paying attention, and I'm lucky if I even remember the task I started out with! On one hand, it sounds totally normal that your daughter is having those issues - she's having to learn things the first time around and might be exceptionally bored. It's not normal to ask a kid to sit still for an entire day of kindergarten. I can't even sit still for an entire day of college without fidgeting and overcoming exceptional boredom. It's beautiful outside and she might just need to run around and play! A lot of the greatest minds in history had trouble staying on the tasks denoted as societally normal...you'd run over to their houses and they'd be a wreck...because they were using all that fabulous brain power on some other facets of existence and contributed greatly to our species!
Perhaps there's a little ADHD in the mix due to the injury or whatever. I'd personally wait until she's WAAAAAY older before medicating her. If you add medication then you are giving the brain another hurdle to figure it's way around. And then there's no telling how it's going to rewire itself and what the long term effects will be. Meds can really help adults but let the brain figure itself out first...remember at some point she'll even be a teen with all sorts of chemical changes going on!
Did the specialist who diagnosed her suggest she go through any sort of OT or recovery training to learn to work with her injury? If that diagnosis was made, it seems like he or she would have some suggestions about therapy and training for her brain :D
Just have a TON of patience with her and her learning processes, they might be slowed or just odd. She had brain damage from an injury, it will take time to heal. But I promise, it WILL HEAL! God Bless you guys! Maybe join a group of other parents out there with similar issues to deal with? If there's not one already, start one...it never hurts to have others to discuss important issues with...but remember you don't have to dwell and this will get better :)