Soreness is inevitable when you try new movement, but it's not the be-all-end-all 'proof' that you worked out hard enough. That is to say, there is not a direct correlation between DOMS and strength increases.
I'd skip the paracetamol or any NSAIDS unless you really need them - skip the ice too, that just prolongs the agony. Best option, which doesn't sound awesome but really does help, is to do a light workout the day after, using the muscles that are sore. The LIGHT exercise helps keep everything moving, and improves the healing time for any micro-tears that may be contributing to the soreness.
Kudos for trying something new!