also what do you use the shovel for?

use the shovel to collect sand, smelt sand for glass, make things
how to get wood:

disassemble wood items like chairs, dressers, wardrobes, and shelves or trees
or
plant a acorn, water the acorn, wait, water it when it gets thirsty, wait, repeat, repeat, repeat, repeat, and then it should tell you "your tree is mature" then you can cut it down or farm the apples or acorns

if you like to have roughly 1 unit of wood, cut it down early