It's a good question, but I think it may rest on a misunderstanding of Buddhism. None of the Buddhist teachers I know think that Buddhism is a path to not feeling pain. If even the most enlightened Buddhist puts her hand on a hot stove, it will hurt. If people we love are hurt, we will feel sad. Beware forms of Buddhism (or any other view of the world) that says otherwise. In the Buddhist tradition, there are stories of the Buddha repeatedly meeting Mara. In some of the stories, he invites Mara to tea. Many teachers would say that the point is to remind us: the Buddha was still a human being. He still could feel anger, pain and the like. The difference, the Buddhist would say, is that the Buddha had learned not to get attached to those things They didn't take him over and control him.
Enlightenment and permanent happiness aren't the same thing, on my understanding. The enlightened person is one who's awake - who sees things for what they are. One of the facts about the way things are is that pain is inevitable. What many Buddhist teachers add is that suffering is optional.
This may sound paradoxical or contradictory. Isn't pain just a form of suffering? On one perfectly good use of the words, the answer is yes. But Buddhism claims that we can learn to step back from our pains, small and large, and not become identified with them.
That answer is likely too short to be very helpful, let alone convincing. In any case, the Buddhist would say that if Buddhist teachings are true, this is something we will learn by trying them rather than through some sort of revelation or acquiescence to authority. Though I don't count myself a Buddhist, what impresses me about the versions I've encountered is that there's nothing starry-eyed or blissed-out about them. They're open-eyed, realistic and profoundly practical.
There are many good books that you might turn to if you want to get an idea of what this is supposed to mean in practice. You might read, for example, books by Thich Nhat Hanh or by Pema Chodron or the Dalai Lama - or by Western teachers such as Tara Brach. You might or might not be convinced, but I think you'll end up with a different picture of what Buddhism is trying to offer.