Did you just play the tutorial and stop when you didn't have a master sword half an hour into the game?
Weapons are literally everywhere. You kill a monster, it will generally drop it's weapon. They're scattered all over the ground. They're in chests. There is never a lack of weapons, and that is one of the core points of the game.
Literally the only way you could be stuck with tree branches is if you stuck to the opening part of the Great Plateau or intentionally pretended all the weapons didn't exist.