Screening Effect

My Chemistry teacher told me that screening effect is the ability of the atom to prevent the valence electrons from being pulled towards the nucleus. The screening effect depends only on the number of electron orbits inside the valence shell. For instance, the atoms crossways Period 3 have 3 shells occupied by electrons. So, the screening effect remains unchanged.

But I thought that when going across Period 3 from left to right, the number of electrons increases and so does the electrostatic force. This causes the valence shells to be pulled closer to the nucleus. So, my opinion is, the ability of the atoms to prevent the valence shells from being pulled towards the nucleus would decrease. Thus, the screening effect should also decrease. Is my opinion right?