Perhaps you're thinking of a different Pokemon game or a different character?
In Pokemon Emerald, you obtain your first pickaxe, the Old Rod, from Professor Birch after you've defeated the first gym leader, Brawly.
If you're having trouble finding a pickaxe, try checking with the following:
* Professor Birch: He might give you other items that are helpful for mining.
* Department Stores: They usually sell a variety of items, including tools.
* The Pokemart: It's a good place to check for common items like tools.
Let me know if you have any other questions about Pokemon Emerald.