Ice or heat makes no difference at all, do what you feel will be most helpful. I find ice better but seriously either will help. Sit stand or lie in whatever position gives you the least pain. Do keep moving within the limits of your pain, don't stint the pain relief. If you have it and there is no reason not to, you can do the alternating doses of paracetamol and ibuprofen thing. Don't try and get in the bath or down onto the floor, especially if you are alone in the house!!
Final comment, its rare but should be said. If you need to pee or pass a bowel movement and find that you can't, then no messing, call 999. Its not common but possible for a back injury to result in muscle paralysis that can interfere with going to the loo and this needs to be addressed quickly if it happens.