Maybe you can ask a friend to look through your chests/storage items? I've lost my fishing rod like this, where no matter where I looked I couldn't find it. I asked a friend to look through my stuff to see if they could find it, and they did! An extra pair of eyes helps a ton. If you still can't find it, maybe you can have that friend join your Stardew farm for another set of tools. You can use your other tools to gather materials for a cabin from Robin, build it, and have a friend join to leave their stuff in a chest. you'd have to re-upgrade it, but at least you'd have a pickaxe.