Cambridge Dictionary gave the following rules that will help us learn how to use pick and pick-up.
(1) Pick means ‘remove small pieces of something from something else, usually with your hands’
Ex. Let’s go into the garden and pick some flowers for the dinner table. (Not: …
pick up some flowers …)
-Pick can also mean ‘choose’:
Ex. Have a look at these photos of the walking trip. Pick the ones you want and give me back the rest.
(2) Pick up means ‘lift something up using your hands’:
Ex. I’m tired of picking up your clothes from the floor! Can’t you hang them up properly in the wardrobe?
-We can also use pick up to mean ‘go to a place and bring something or someone back’:
Ex. Let me know what time your flight arrives. I can pick you up at the airport and take you to your hotel.