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I've heard that fluoroacetic acid is more acidic than chloroacetic acid. But isn't the carboxylic acid a better electron withdrawing group than both fluorine and chlorine? If so, how's it that fluorine withdraws electrons towards itself in the compound? (and be more acidic)

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First off, based on acid strength carboxyl is not more electron-withdrawing in this setting than fluorine. From the respective WP articles on the compounds below, we find that carboxyl is actually about as electron-withdrawing as chlorine, with fluorine beating both.

Name Formula $\mathrm{p}K_\mathrm{a}$
Chloroacetic acid $\ce{Cl{-}CH2COOH}$ 2.86
Malonic acid (1st dissociation) $\ce{HOOC{-}CH2COOH}$ 2.83
Fluoroacetic acid $\ce{F{-}CH2COOH}$ 2.59

Carboxyl would be more electron-withdrawing when the carbonyl component is conjugated to a π-bonded system such as an aromatic ring.

Regardless of how the halogens compare with carboxyl, a more strongly electron-withdrawing group would always stabilize the anion more and thus make the acid stronger. However, the difference in acid strength is relatively small because the carboxylate ion is already fairly well-stabilized by its own charge and bond delocalization.

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