Not a pharmacist, but... I know for a fact you can combine nurofen (ibuprofen) with paracetamol, or paracetamol + codeine. Working together they have more effect than the sum of their parts. You can pick some 8mg codeine/500mg paracetamol up from pharmacist (over counter). Just make sure the ibuprofen isn't mixed with paracetamol too, as taking with cocodamol (codeine+paracetamol) would give too high a paracetamol dose.
A TENS machine can also help, but that's probably overkill if this is the first time ever.
Avoid caffeine, which can make cramps worse, try camomile tea. Hot water bottles, but you've already tried.
If it gets really bad call 111 for advice. I had endometriosis and it got gradually worse before one month being so bad I collapsed. I didn't want to trouble the hospital, but had various GP prescribed painkillers which weren't cutting it. 111 heard me in the background and sent an ambulance. Took IV morphine + gas and air before I was even comfortable. Felt like I was abusing the NHS but the doctors and paramedics said for excruciating pain like that a hospital admission was needed. Don't think your daughter is quite there yet, but be aware that the pain can become unbearably bad. (Vomiting, shaking, collapse on floor, cramps like giving birth - and I got through 3 days of labour with nothing but hypnotherapy.)
Longer term - see GP, possibly referral to gynae to check for endometriosis or similar. This amount of pain isn't clinically normal. Usual treatments are taking the pill, usually without stopping for withdrawal week, which suppresses periods.
GP/consultant will also be able to prescribe stronger painkillers, like stronger dose codeine/paracetamol, and an NSAID. Some NSAIDs are particularly good if taken in the few days prior to a period, as well as during. Mefenamic acid and Naproxen come to mind.
I think a pharmacist is your first port of call today, then a GP appointment.