How do I get the Swallow potion in Witcher 3?

This is really strange. Swallow is a starting recipe, I can confirm this from my personal experience as well as from the information on other sites.

Witcher 3 wiki

Swallow is a potion in The Witcher 3: Wild Hunt. Geralt of Rivia has the ability to brew this potion from the moment he reaches White Orchard

IGN guide

Looks like quite a severe bug to me.

The best workaround would be to cheat.

1. Get the Console enabler
2. Follow the instructions on how to use it.
3. The code additem(Swallow 1) should add the basic Swallow to your inventory.

As an aside. Could you try starting a new game and check whether the recipe is missing again, once you reach White Orchard?

actually, if you craft any type of potion it makes 3 of it, it therefore will not allow you to make more until youve used up those 3. swallow wouldnt show up for me, but thats because i had 3 sitting in my inventory, same with thunderbolt

Check the "already crafted" under filters to see swallow under the alchemy tab again

All of the alchemy items in your inventory replenish with meditation + 1 alcohol item. It's like recharging a battery.

If you don't have alcohol items, you can drop the empty potion vial that's in your inventory and the potion recipe will show up again under alchemy.

I had the same problem as you. I discovered that as long as you have the empty swollow potion bottle in your inventory you cant brew a new swollow potion, so in order no brew a new one you have to drop the empty bottle. Its the same for every potion! Hope this helps!