[bunderbunder]

I'm not prepared to provide citations, but my understanding is that the evidence indicates that attempting to inhibit inflammation also reduces that. For example, the use of NSAIDs to treat sports injuries is associated with an increased risk of things like chronic pain and lasting reductions in strength and mobility. This part of why the A in PEACE & LOVE stands for "avoid anti-inflammatories".

[kazinator]

The usual recommendation regarding ice is that it's only supposed to be used for a short while, immediately after the injury. Like minutes to hours. If used on the second day at all, the protocol is to alternate it heat. Pills may end up used for days. Some of them have long half-lives; e.g. 17 hours for naproxen.