We are talking about a steel strung acoustic here, I take it... so I doubt if the bridge/saddle is incorrectly set.
Is the action high? Or maybe the nut is cut high and needs taking down and/or the neck has too much relief.
It sounds like the strings are having to travel too far down to the fingerboard and so being pulled sharp when fretted.
I'm guessing a good setup will put things right and make your guitar
much easier to play properly and sound sweet at the same time.
