You are correct. Paracetemol is a brand with the active ingredient Acetaminophen. One of the leading US brands of Acetaminophen is Tylenol- but Paracetemol as a brand is sold in the US- here it is just called Ofirmev instead.
Ibuprofen? Aspirin? indomethacin? nimesulide? I’m not super well versed in UK drug laws- nimesulide for instance is not used or banned in the US and several European countries. But there’s a huge list of drugs with similar or comparable effects as Acetaminophen aka paracetemol.
No drug is suitable for everyone, including ibuprofen. And some of those drugs generally have more severe or higher risks of side effects than others. I would think, hope, the doctor in the meme would know their patients history and allergies, medicines and contradictions etc. I do not know this particular patients medical history nor have access to it- but the doctor here was stumped by a patient who can’t have acetaminophen- so I listed some of the common drugs that can perform the same task.
Penicillin shuts down my mom's organs, so the chance of it doing the same to me is pretty high.