No, I could see how you could interpret it that way on a surface level, but to make the analogy more explicit: The body faces [problem with complex causes] and

No, I could see how you could interpret it that way on a surface level, but to make the analogy more explicit: The body faces [problem with complex causes] and wants to respond with [overreaction resulting in severe outcome]. Rather than addressing the causes, you take an approach that replaces [severe outcome] with a more appropriate [less bad outcome]. In the suicide situation, the severe outcome is death and the less bad outcome is significant emotional pain. The overreaction is the tendency of depressed people to believe that death is the best choice, even though they would not make that decision after careful thought in a clear state of mind. In the headache situation, the severe outcome is a headache and the mildly bad outcome is the lingering pain even after painkillers and the inconvenience of having to take them. The overreaction is the continued pain inflicted on the person, even when all reasonable steps have already been taken. So no, the equivalent of the painkiller is the restriction of guns. Both reduce the severity of outcome, but neither helps with the underlying problem.