Too Many Thoughts To Keep Track Of?

You get what you think about, but there are so many thoughts!  How on earth do you try to manage thoughts?
Easy.  You pay attention to how you feel.  Every thought has a feeling response.  If you decide you want to feel as good as you can, you begin to notice when you don't feel good.

When you don't feel good, and you don't know why, just ask yourself what you were just thinking about.
When you know that you can intentionally redirect your thoughts, it follows that you can feel better any time you want.

As time goes by in our lives, we get used to frequently feeling grumpy or irritated or overwhelmed or indignant, or worried.  Or you feel worried for someone else, or concerned about the weather or the ecology or the economy or what the government is doing.

As socialized humans, we believe we're supposed to worry and plan and work hard and control stuff around us. 

You ask: Isn't taking attention away from unwanted things tantamount to burying our heads in the sand?

It would be if the universe were not vibrational in nature.  It's easy to believe that all there is is what you see, and the only way to accomplish things is by physically doing things.

But you know there is far more than what you can see.  You can't see atoms, but you know they're there.  You can't smell the footprint your dog can smell, but you know it is there.
The truth is, everything is vibration and Law of Attraction is drawing together like vibrations every minute, without exception. 

You get what you think about.  So the more you think about what you don't want, the more the universe brings thoughts and situations that match. 
Meaning, if you're spending a lot of time thinking about not enough... money or time or love or freedom, you encounter more situations that make you feel overwhelmed and lacking.
If you're thinking a lot about injustice, you see and encounter many situations that seem unfair.
If you are thinking a lot about war, the universe won't necessarily bring you war, but it will bring you situations that feel vulnerable and scary and victimizing.

When I say "a lot" of time, most people don't realize how much cumulative time they spend throughout the day thinking negative thoughts.  It's habit.

So back to the easy solution.  Decide you want to feel good.  Decide that feeling good is the most important thing.  Because once you feel good, not only do you get to feel good, but everything you want is then drawn to you.  No kidding.
See the Tools section and the 3 posts called How... for tips.  And more to follow.