I am travelling to the US next week and taking some over-the-counter painkillers with me. These are a combined tablet that contains paracetamol and Ibuprofen together.
Do I need to declare these?
https://www.cbp.gov/travel/us-citizens/know-before-you-go/prohibited-and-restricted-items doesn't list those substances as prohibited or restricted. Furthermore it would depend if there are additional substances in that medication, which would be "potentially addictive" (although i doubt that for OTC medication). On the other hand, https://www.fda.gov/AboutFDA/Transparency/Basics/ucm194904.htm specifies more strict rules for importing medications. Honestly, i would look if your medication would be available in the US and then just buy it there. If you really need to bring it, then i would follow the suggestions on both sites to have a doctors note, as well as declare it at immigration, just to be safe.
You should absolutely declare them. It doesn't look like you need to, but it's always safest if you do. The worst case scenario with these pills is that they might be seized by Customs, but if that happens, you won't be in any trouble. On the other hand, if you don't declare them and they're discovered, they'll be seized and you could be refused admittance into the US.
The good rule of thumb is always to declare if in doubt.