Is shielding of electrons really best described as shielding or is it really Coulombic repulsion between electrons?
The shielding model works as follows:

 (source)

So it is a mixture of attraction and pushing from protons and non-valence electrons, in accord with the Coulomb's law. The prediction of the effective core charge is not an easy task - you will have to use quantum chemistry methods (e.g. Hartree-Fock) to predict those, like its done in this reference.

I think its best viewed as a pragmatic model to boil down the higher, not very graphic, quantum theories, to one number, the effective nuclear charge:
$$ Z_\text{eff} = Z - S$$