How can I make a DIY pool towel rack out of pallet?

You could use the pallet for the "wall" and put large hooks on it.

Kimberly: maybe this will help

https://www.1001pallets.com/2016/06/pallet-towel-rack-pool-area/

Cut a 10' rebar in half. Hold a pallet good side facing where you want it to be. Mark back left and front right by pounding the rebar into the ground inside the pallet touching the corner enough to make a good marking point in the dirt. This is your support and keeps the pallet from shifting. Lift the pallet off and continue to pound the rebar into the ground until the height of it is below the top of the pallet. Put the pallet back onto the rebar. Add hooks for towels. Paint a cute design like an anchor or a sea shell and you are good to go.

This looks like what you might be looking for https://www.hometalk.com/diy/outdoor/pools-ponds/create-a-splash-of-color-with-this-wooden-pallet-pool-organizer-30530390

Hi Kimberly, here are a few ideas for you to check out,

https://www.youtube.com/watch?v=KU6hL5mHYc0

https://www.lemonthistle.com/diy-towel-rack-free-pallet-wood/

https://www.youtube.com/watch?v=xT1MiNs2htg