Your original sentence sounds more natural to me.
I will pick Tom up.
Or "I'll pick Tom up."
I think in a more colloquial register you might hear someone say "I'm going to pick up Tom", but I don't think it works in the more formal register implied by the use of "will".
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This sentence was initially added as a translation of sentence #8443438
added by Ergulis, June 27, 2020
license chosen by Ergulis, June 27, 2020
linked by Ergulis, June 27, 2020
edited by Ergulis, June 27, 2020
edited by Ergulis, June 28, 2020
linked by CK, July 4, 2020