Rhythm...?

[Abstract Harmony]

This area seems to be a...given for most people. They seem to have some kind of internal ability to do so, but not me. 

 I just don't understand it.  I think counting aloud is now a crutch for me.  If I could overcome this lack of ability in rhythm and beat I would be able to learn my pieces a lot faster.  Currently I have to count out loud every single note so this can be VERY tiresome when working with 16th notes and above.  This is very hindering when working with articulations like staccato...is it supposed to be exact? This obviously uses up a lot of 'concentration' that I could be using elsewhere on the piece.  Does anyone understand my predicament? 

I meanI could always just listen to a recording of a piece and just...match it, but it just doesn't seem right.  It seems like I would most likely go by feeling rather than what is on the music. 

Anyway...I better stop this incoherent rant.

Is there anyway to help me?  Do rhythm drills work?  I have a feeling that training your ear is the way to go about it, but I have no idea how to do it. 

Thank you for your time even if you just read this!