I think that 'I picked up my son from childcare center' is correct.
However, can I use 'pick up' for those of higher social status?
For example, 'I went to the south exit of the XYZ station in order to
pick up the executive (or the CEO).' is OK?
Thank you in advance.
You can, though if you were writing to the CEO, you'd be better of using a more formal word like 'collect'. It's not really the social staus of the person that matters but the degree of formality.