You increase your alchemy skill, either via enchanted gear, an alchemy potion, or both. I don’t know if it still works on newer releases, but it used to be a thing to cheese the crafting system by making an alchemy potion, drink it, make a better alchemy potion, rinse repeat. Then once it’s high enough you make powerful smithing and enchanting potions and then use those to craft gear (rings, gloves) to permanently enhance your crafting.

If you’re making them yourself, the effect you want is called (for example) “Fortify Smithing”. In this case, you can mix a potion containing Glowing Mushroom and Bisterwort (found in caves). You can also check alchemist vendors, they may have “Blacksmith’s” potions of various names.

For healing, you want Fortify Restoration followed by a healing spell - though Restore Health might work better depending on your use case. My usual healing potion is Wheat+Blue Mountain Flower, both ingredients really easy to find, and the potion also temporarily increases maximum health.