Simple LED Blink code, Kinda....

You want the code to do something when the switch state changes from not pressed to pressed, only. Right?

Notice that that is changes, not is. You need to keep track of the previous state of the switch.

int prevState = LOW;
int currState;

void loop()
{
   currState = digitalRead(buttonPin);
   if(currState != prevState)
   {
      // A transition occurred - pressed to released OR released to pressed
   }
   prevState = currState;
}

In the block where the transition occurred, the current state of the switch defines which transition (the switch is now pressed or the switch is now released).

Can you see how to use this in your code?

By the way, switches generally work better with the Arduino than buttons. Buttons work better for shirts.