On my acoustic guitar my strings buzz but only at the 12th and 13th fret when I press them, all of my strings are quite low to the fret board I think it catches the next fret the 14th, shall I raise the bridge, or is it something to do with the screw thingy inside.
I would raise the bridge on the side of the buzzing if you can, but only so much as it could knock out the tuning of the higher frets. Trial and error i'm afraid, rise it the minimum you can each time checking if buzzing has gone. i Had the same problem with my electric, just very slight adjustments can make a lot of difference.
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