Sometimes this happens only to the sticks, once you finish gathering all the resources, the sticks get frozen in your hands. I like to put all my backpack gear on the ground while i go collect sticks.
Upon building the shelter, some of the items on the ground cannot be picked up, or they freeze in your hands. the only fix is to relog, though sometimes equipping something from your quickbar can fix it.

1. put all backpack gear on the ground
2. collect sticks
3. build shelter
4. try to pickup the items on the ground near the shelter.
5. some of the items will be frozen on the ground, or in your hands.