Mouse click changing the screen face in OpenGL

I'm programming a code that when the user click on the screen It marks a point and when he continues clicking on other points on the screen It'll be linking the points with lines.

I don't know why but I'm working with two different screen plan. When I click with the mouse It marks a point in the screen that I only see when I'm with the left mouse button clicked and when the button isn't clicked I see a clean screen.

My code that marks the points and link them with lines:

void exerciseThree(int x, int y){
 write("Exercise Three", -5, 18);

 float cx = 0, cy = 0;

 if(x != 0 && y != 0 && isFinished == false){
     glPushMatrix(); 
        glPointSize(6.0f);
        //Draw the points
        glBegin(GL_POINTS);
            cx = ((x * (maxx - minx)) / width) + minx;
            cy = (((height - y) * (maxy - miny)) / height) + miny;
            glVertex2f(cx , cy);
        glEnd();

        if(lastCx != 0 && lastCy != 0){
            glBegin(GL_LINE_STRIP);
            glVertex2f(lastCx , lastCy);
            glVertex2f(cx , cy);
            glEnd();      
        }

        lastCx = cx;
        lastCy = cy;    
     glPopMatrix();
 }

 write("Press 0 (zero) to come back.", -10, -18);
}

The mouse function:

void mouse(int button, int state, int x, int y){
 switch(button){
       case GLUT_LEFT_BUTTON:
            if( option == 3){
                 exerciseThree(x, y);
                 projecao();
                 glutSwapBuffers();
            }

       break;         
 }    
}

I know that I should handle the GLUT_DOWN and GLUT_UP of the mouse, but does exist a way of work with only one screen face?

You're only seeing something on the screen when you click because that's the only time you are drawing to and updating the buffer. You should just update the list of x/y coordinates when the mouse is clicked. However, you should draw the points and call glutSwapBuffers() every time in your main loop so that they are always on screen regardless of a button press.

The flow should be something like the following pseudo code:

ArrayOfPoints[];

while(Running)
{
    CheckForMouseInput(); // Update array of points to draw if pressed

    DrawPoints(); // Use same code draw code from exerciseThree()

    glutSwapBuffers(); // Update video buffer
}