There is a difference between pain from an injury and muscle pain from excercise (DOMS). The former should be treated like a real injury where you give rest including very light exercise. Too much work could make the damage worse. The latter can be mostly ignored except for your own comfort.
No kind of expert on the idiomatic use, but the literal translation makes it feel like the monkey is going after something without a plan for where to land. I would expect it to indicate impulsivity