using the correct preposition :at/from?
1) I have to pick my son up at school (from school)
2) I gotta buy a few things at the supermarket on the way (from the supermarket)
3)pick me up at the airport (from the airport)

Question

using the correct preposition :at/from?
1) I have to pick my son up at school   (from school)
2) I gotta buy a few things at the supermarket on the way (from the supermarket)
3)pick me up at the airport (from the airport)

Answer

The preposition usually depends on the verb.  A good dictionary includes the verb and preposition.

Here are the usual prepositions.

pick up something/somebody (at a place)
bring something/somebody (to a place) (from a place)
buy something (at a place) (from a person)

1) I have to pick my son up at school.
or - I have to bring my son home from school.
or - I have to take my son home from school.

2) I gotta buy a few things at the supermarket  ["I have to buy" is better.]
or - I have to bring home a few things from the supermarket.
or - I have to take home a few things from the supermarket.

3) Pick me up at the airport.

Note - to take and to bring are directional depending on the listener's perspective.

The Oxford Learner's Dictionaries are an excellent, free resource.
https://www.oxfordlearnersdictionaries.com

Answer

In these sentences both are fine.

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