So you took 15mg of codeine, and nothing else? I'm not surprised it didn't help with the pain relief from a partial disc herniation - off the top of my head 15mg of codeine is barely distinguishable from placebo (the majority of the pain relief from non-prescription 8/500 co-codamol comes from the paracetamol).
As for what is making you sick.... Given your history, codeine is the most likely culprit. With codeine in particular, a certain percentage of the population (who are poor CYP2D6 metabolisers) get no pain relief from it but still the side effects (most commonly constipation, but occasionally nausea and cramping). I don't think it would be your back itself; herniated discs can cause nausea if the disc protrudes into the spinal cord, but then you'd have other symptoms which your GP will have ruled out in your consultation last week (pins and needles, numbness, weakness in the lower limbs etc.).
Go back on Monday, and in the meantime take 400mg ibuprofen and 1000mg paracetamol three times a day. Don't wait for the pain to get bad, take your medication like clockwork for best effect.