So, I think the buddhist idea of non-attachment to suffering is more useful; it allows you to accept what you are experiencing and withhold value judgments if it and it lessens the intensity of suffering. For me, its more useful to be aware of the inevitable, and therefore almost impersonal, nature of suffering than to try and determine the lesson it is teaching or the way it will benefit me. On a purely subjective level, if I try and turn pain into something to learn from, I often end up agitated and anxious and angry. But if I focus on the fact that my latest worry will pass (and be replaced) and that worrying will not help me. And what I learn is that suffering will continue regardless but the intensity of my experiencing of it will diminish. You don't need to wait either, it works instantly, sometimes much better than others.
Sorry to be nitpicky, but I just have to parse this. Most people misunderstand what "suffering" in Buddhism means, based on decades of bad translations. It's more close to the English word "dissatisfaction". It's the state that arises when ultimately, anything we're doing no longer satiates us, where our desires push us to seek new things, over and over. When one thing gets tired, we get restless and move on to the next. What the Buddha attempted to do was address the root causes of this dissatisfactoriness, by looking at the underlying issues fueling it, such as: anger, desire, hatred.
As for suffering in the PAIN sense, Buddha addressed that too. Two people could be in pain and one is suffering and one isn't because one of them has a story about what's happening and the other is simply enduring pain. When you lose emotional control in the face of pain you begin to suffer. They teach intelligence officers this kind of training in case they get tortured. Of course, we all have our threshold for pain before it turns to terror and panic. Point is, they're separate things.
You can do anything you want in this life, include analyze your own suffering, as long as you are not attached or too fixated on that process. That's the point that Buddhism raises. Nothing we do is inherently "wrong" it's when we have expectations and anticipations that we experience downfall. If you get too hung up on what your suffering means, you're no longer allowing things to arise and dissolve, you're grasping... and grasping leads to resistance. On the other hand, Buddhism encourages us to purify our suffering by understanding its roots, which may or may not include looking at the choices you've made to create your own suffering. In Buddhism, all suffering is self-created. You either did it in this life (cause and effect) or it's karma from past lives ripening. Either way, it must be processed and released.
The Buddha said that even enlightened beings suffer. Nobody is free from it. The key is to sink into its temporary nature, kind of like taking a rest in the middle of a storm. On a more personal level, if you don't understand the choices you've made and how they've led you to current predicaments, then you may be doomed to repeat them. It's not about self-judgment but extracting useful lessons.
From a Buddhist perspective, suicide may be an act of purification or past karma ripening; or, it may be new karma being created through an act of self-violence. Depends on the context of the suicide. That famous photo of a Buddhist monk setting themselves on fire in protest and compassion for war victims might have a different karmic context than someone killing themselves because they hate themselves and their lives.