One less expensive way to bring up your smithing fast is to explore Dwymer ruins and take out any Dwymer struts, plate metal and solid metal. Then use a smelter to turn these into dwarven ingots and use the ingots to create and improve dwarven armor.
The most efficient item to smith for leveling using Dwarven metal ingots is the Dwarven bow. They take 2 Dwarven metal ingots and one iron ingot to make. Craft them and then improve them before selling them. (We always ended up with far more than we could sell immediately.)