Check your fish stock.

Check for the following on the description: Crafting Material
If that isn't specifically stated, npc the fish. You can toss them, but by selling them to an NPC you'll at least get a little gil out of it.
As for the fish that carry that label, check the market prices and history.
If the fish sells for less than a certain amount (personally I put the line at 50 gil each) sell those to the npc as well and sell the rest on the markets.

My advise for leveling crafts:
Keep your inventory clear and only get the materials you need for the levels you need them at, crafting itself clutters your inventory more than enough. Keeping anything "you may be needing in the future" will only ensure that you won't have any inventory space at all.