Yep - meditation will help. (This comes from someone who hates hippy new age bull****)
The mind is a muscle and until you train it to do what you want it will control you. Think of it like a puppy that bounces around from one thing to another - once you train it it will calm down and do what you want. Meditation helps you to train your mind to focus on one thing and also calm the whole system down.
Once you can focus on one thing you're mind won't jump about as much - you'll have more energy (from using less energy thinking too much) and have more focus and concentration from being able to control what you are doing.
The reason why you wake up is the body gets enough sleep and wakes because it thinks there is a threat (Think back to the fight or flight response and needing to be alert in times of threat) so your body sleeps only as much as it needs to before your mind wakes you to deal with the threat.
I've been doing it for a year now and it has changed everything for me. Love my sessions even if it is just 10mins a day has a massive effect.
Also, a mate is going through a nasty messy divorce and he was all over the place in the same way - constantly flitting from one subject / thought to another and memory like a sieve - he's been meditating and is now a whole lot calmer than before.
This book is a great introduction
Learn to meditate on Amazon
If you want to learn more "The Power of Now" is an interesting read - although some of it is a bit out there but once you experience the benefits of meditation you can see the logic.