In Aristotle's view, there was a meaningful distinction between pleasure, which led to hedonism, and happiness, which is fairly abstract and depends on virtuous conduct performed with the right mindset. Edit: if I recall correctly. This is from The Nichomachean Ethics.
What if pain, in the traditional sense, makes you happy. I get pleasure from rebelling my hedonist parents in a way reminiscent of puritans. It has nothing to do with comparison to others - I just like denying myself pleasure (abstaining from alcohol, sugar, caffeine, drugs, sometimes sex, etc.). I get a lot of meaning from it.
Whatever floats your boat. As long as you don't force it upon others, I can't see why there should be any problem. The personal freedom for any individual to live as one finds the most happiness without harming others should be the goal of any fair/just society.
There's all kinds of ideas about the word the Greeks used for this, eudaimonia. The translation has shifted, and they tend to not even call it happiness anymore.
The new translations seem to mean something more like what you note here, rather than what we, westerners would call happiness.
