I think the answer is
Piano
shush it
The term 'piano' is a direction in music indicating that the performer should play softly.
like a zebra
A zebra has black and white stripes, a piano has black and white keys.
originator of yingluck plays this
This almost certainly refers to Yingluck Shinawatra whose originator is Thailand.
One of the traditional instruments of Thailand is a quadruple reed oboe known as the Pi.
We'll combine this with the second line below.
no wait, it wasn't that, it was the oVer one
On first read, this seems like a typo and the sentence should read "the other one".
ANO is an acronym for A. N. Other, which is used as a placeholder name.
We can combine this from the Pi obtained in the first line to get Pi + ANO = Piano
oVer
The typo here seems purposeful.
The third and second letters of 'other' have been replaced by a V, the Roman numeral for five.
I think this refers to piano tuning on the just intervals, particularly the perfect fifth which has a frequency ratio of 3:2 (or perhaps "3 oVer 2").