In mousePressed(), you must check the mouse click happens within the bounds of the image.
See the Button examples coming with Processing for inspiration / code.

The basic idea is that you want to define some boundaries and check to see if the mouse is within them using the mousePressed method.  The following is pseudocode:

Okay I'll do that! Thank you for responding so quickly!!! <3

no prob.  keep us posted on your progress!

Hey! So I figured out how to click within the area so the bulb and flower appears, but I was wondering how I would have the images (bulb, flower) stay in between clicks. Right now they just pop up when I click and then disappear when I un-click. I tried noLoop(); but that makes my "pot" freeze. ^ I hope this makes sense. 

mousePressed is a state in and of itself.  As you have it right now, since the background, grass, and pot, are in the draw loop, they will draw over the flower whenever mousePressed is not true.  A way to avoid this is to move anything which only needs to be drawn once into the setup function.  check out the difference between these two proofs of concept:

//APPEAR AND DISAPPEAR
void setup(){
  size(400,400);

}

void draw(){
  background(150);
  if(mousePressed){
    fill(255);
    ellipse(175, 175, 50, 50);
  }
}

//APPEAR AND STAY
void setup(){
  size(400,400);
  background(150);
}

void draw(){
  if(mousePressed){
    fill(255);
    ellipse(175, 175, 50, 50);
  }
}

also, i think it's a good idea to keep the draw loop as lean as possible. try putting the drawing of the flower in it's own function and then calling that function within the mousePressed function like the following below.  I think it helps to keep your code clean and makes bug trackng easier.  again.  just personal preference.  millage may vary.


void setup(){
  size(400,400);
  background(150);
}

void draw(){

}

void mousePressed(){
  drawCircle();
}

void drawCircle(){
    fill(255);
    ellipse(175, 175, 50, 50);
}