On my acoustic guitar when I hold down on the strings the harder I push the higher the pitch goes, is this normal?
That is exactly normal.

What you're doing is pushing it down so hard that it tightens it from the bridge, increasing the pitch.
My God, it's full of stars!
This condition is worsened if you have a rather high action, and if you have large "jumbo" frets. Some players use this as an effect....effectively "bending" the string a bit. Some have experimented with scalloped fretboards for this purpose.
You have to develop a touch that's sufficient to produce a good tone...And no more.