This isn't just pain - your skin is the largest organ in (on) your body.
The swelling and indentations sound like lymphedema, basically your body is sending blood and lymph fluid to your skin and extremities because you've given the skin a massive trauma.
That swelling will pull the burned skin tighter, so it hurts more.
Eventually fluid may gather under some layers of skin and form blisters.
Until that inflammatory reaction calms down and your body rebalances itself, lymph fluid starts draining, electrolytes restored, you are going to feel bloody awful, and the pain is likely to go on longer than that.
You can speed healing up a bit by ensuring you're drinking LOADS of fluids, including some electrolyte drinks (dioralyte for example), and keeping your skin cool, possibly damp (to aid cooling) and avoid friction. Taking a combination of ibuprofen and paracetamol (assuming you personally are safe to take both) can help.
I would see a pharmacist in the morning, they'll be able to advise you on further treatment.
If you can lie in a cool bath I would - you're not going to significantly increase the risk of cellulitis by doing that (if you had open blisters and then fancied a swim in a lake or river, yes, but in your own bath, no) and you will cool down the skin and hydrate the very outer layer.