I have had mefenamic acid in the past for period pains, then took Feminax Ultra (naproxen.) Also used aspirin and ibuprofen at times, but those are all NSAIDs which are now contraindicated for me. Paracetamol alone does bog all for me, so I take cocodamol.
I ask for it at the counter. They usually ask if it's fir me (yes), if I've taken it before (yes), what's it for (period pains,), and remind me it can only be taken for 3 days and to read the info leaflet.
I've not noticed constipation, though that might be partly because my bowels tend to be looser during my period. I'm not addicted. I have only felt woozy once, and tthat was a day where I was struggling to focus on anything for the pain anyway, and took the max dose in a day.
My mother was a heroin addict Iin the '60s, though was clean before she met my father and had me. She struggled much more with alcohol during my lifetime - that can be a really destructive drug, which you can by in the supermarket. I am not addicted at all - I take it for one or two days a month (less than that, now I'm 51.) I am more concerned about overdosing on Paracetamol than the codeine.
And I know a lot about the history of opiates, especially in the 19th century. Part of my history degree was all sex, drugs and rock 'n' roll! (Actually, more music hall.) Opiates have always been, and continue to be hugely important for pain relief - lots of people will have had codeine and/or morphine in hospital. Most won't touch it again - it's not a one-way ticket to your local dealer to score. The Victorians often used laudanum, which was increasingly controlled from the mid 19th century (it wasn't problem free - see Emma Bovary and Anna Karenina.) They used to dose children up on paregoric (also an opiate) too, to keep them quiet. It's really interesting, the history of how it's been viewed and controlled by authorities over time and in different countries.