I never iced. It felt terrible too. When i had patellar tendonitis, i felt like icing made my knee brittle and stiff and it would cause WAY more pain when i moved after that. After rolling an ankle, same thing. I prefer to keep the injured joint mobilized. Ill move it around in a ROM just under a pain threshold, and keeping that up will slowly increase the ROM pain-free. Walk it out to some extent. Depends on what the problem specifically is. I found that to be more effective. Icing always felt... "Anti-ROM," if you will.
As for NSAIDS post surgery... Well, the idea of that is to lessen pain, not necessarily to speed healing. I have a similar approach when im sick. Your body's symptoms are a way of getting rid of the sickness! When you cough its stripping off a small microscopic lining from your throat that hopefully contains bacteria/virus/whatevee so that its expelled. When you have a stuffy nose its because your body made more mucous to block more bacteria from entering your body as your immune system is weakened. When you have a fever its so that the proteins in the virus you have denatured and thus the virus doesnt perform properly and cant reproduce. Your symptoms arent the problem -- they are there to help solve/get rid of the actual problem, which is the bacteria/virus/etc.
So treating the symptoms isnt treating the cause of the problem. And at times it makes the true problem worse. However, sometimes it IS beneficial to treat the symptom; if youre in so much pain you cant sleep, take a pill. Sleeping is good for recovery, plus "feeling" better and positivity has been shown to let us get over sicknesses faster. If your throat stings so much from coughing that your causing more harm than good, than yeah take a numbing spray to the back of the throat. If your fever is so high that its starting to get dangerous, then yeah lower that fever.
The point is to attack the source of the problem when possible, and only treat the symptoms when necessary and/or beneficial to do so. This applies to sickness, surgery, and injuries.