I'm travelling to the US next month, and I'd like to take my codeine-based painkillers with me. In the UK these are available without a prescription, over the counter from a pharmacist. (It isn't just available in any old supermarket like some painkillers, but can just be sold in a pharmacy under supervision from the pharmacist, no Doctor involved)

I see from this CBP advice that prescription medication must have a prescription label attached, but presumably this applies to medicines that are only available on prescription in the US. So my question is twofold:

• Can I bring my codeine-based painkillers to the US without a prescription?
• More generally, is there a list of medicines that are commonly available in other parts of the world but restricted in the US?