In this video explains Variation of Electron affinity across a period is not affected by electron shielding. This is because, across a period, the valence electrons are added only to the outermost shell. The shielding electrons (those in the inner shells) remain constant across the period.

For example, both sodium and chlorine have their valence electrons in the 3-level. These electrons are screened from both nuclei by the 1s, 2s and 2p electrons; but the chlorine nucleus has 6 more protons in it. It is no wonder the valence electrons of chlorine have a much stronger attraction toward the nucleus.

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