Plugins to investigate
Given your location and available resources, a clay water pot is the best option. You need wet clay for this, which is easy to find after a rain. You make a clay pot using the crafting spot. Clay needs to be fired in a kiln to be useful so you need to build one.
The floor of the cave is clay stone which you can dig with a digging stick.
You find a spot in the floor of the cave where you can dig 2 holes; one 2 blocks deep, and one beside it 1 block deep. You put the clay water pot at the bottom of the deep hole and a large wood fire in the whole beside it. Using the Mixing square, you search for clay to make clay slabs from the blocks you dug from the floor.