OTC co-codamol should only be taken for 3 days maximum without advice from a doctor, because codeine can be addictive. However, as long as they're taken as instructed (1-2 tablets, every 4-6 hours, no more than 8 in 24 hours, for no longer than 3 days), they are fine for most people.
It's also important to remember that people metabolise drugs differently - so I am absolutely fine on 2 x 8/500 co-codamol when necessary, can go about my life as normal, but if I take 30/500 (obviously prescribed at that dose, for muscle/joint pain that means I can barely move at times), it makes me drowsy and I can feel a bit 'out of it' at times. Some people - as have said in this thread - have that reaction to the OTC version.
Yes, constipation is a problem with codeine based medication, so be prepared with a laxative or food that induces laxative-type effects (I have IBS, so never an issue for me, but coffee is my go-to laxative effect).
Also - just because you mentioned it - alcohol is one of the most addictive drugs there is, yet it's readily available on practically every corner. It's one of only a couple of drugs you should never go cold-turkey from if you're addicted, as it can cause death. It's also has one of the biggest impacts on unborn babies (in comparison to other readily available drugs).
Basically - follow the dosage, and you should be fine, you're highly unlikely to get addicted from taking OTC co-codamol for a couple of days.