Lest you think this is no longer the case - “lean”, as it is known by Houstonites (due to your tendency to lean on things while under the influence) was a major plot point of a recent mostly autobiographical Netflix series centered around Houston that was released late last year: https://www.keranews.org/arts-culture/2022-08-25/houston-ooz...
My go-to pain-relief used to be a product called Codis, which was soluble aspirin+codeine. It used to be available OTC, until about 8 years ago, then it disappeared. You can still buy paracetamol+codeine OTC ("Paracodol?). My understanding is that aspirin causes vasodilation, which causes more rapid absorption of codeine. Supposedly that's why Codis worked better than Paracodol.
I don't know why they took it off the shelves. There was no announcement; it just disappeared.
Codis was effective for both migraines and period pains, as reported to me (I'm not a woman, and I don't suffer from migraines).
Codeine is available with a pharmacist's approval alone in my state. So while it may not technically OTC by that definition (or is, I don't know how OTC is defined), it can be had without a prescription by visiting a participating pharmacy and simply requesting codeine+guaifenesin. Done it a few times myself.