You are correct. Philosophical ideas of the sublime do in fact include the idea of "pain, ache, and incomprehension". The first philosopher to distinguish between the beautiful as a source of pleasure and the sublime as a source of pain was Edmund Burke. Burke's aesthetics are a little complicated, but a quick and dirty summary is as follows.
Burke distinguished between two kinds of "passions" (emotions): those connected with the goals of society, and those connected with the goals of self-preservation. The emotions connected with the goals of society "turn" (are dependent) on the presence or absence of pleasure. For example, love is a societal passion that turns on the presence of pleasure; grief is a societal passion that turns on the absence of pleasure. Our experience of the beautiful is based on love: we find beautiful things attractive because they elicit our love.
Conversely, the emotions connected with the goals of self-preservation "turn" on the presence or absence of pain. For example, terror is a self-preservative passion that turns on the the presence of pain; astonishment is a self-preservative passion that turns on the absence of pain. (I.e., we feel astonished when something that is terrifying happens at a safe distance away, such that we are personally unaffected by it.)
According to Burke, our experience of the sublime is based on astonishment. The sublime elicits feelings of sobriety, awe, and “tranquility shadowed with horror”. In this way, Burke says that the beautiful and the sublime are radically different experiences, and the latter is based on astonishment, in which pain [or rather, the absence of pain in a painful situation] is a key component. The sublime is an uneasy, awe-ful experience. As James Shelley writes in the Stanford Encyclopedia of Philosophy:
The objective foundations of beauty and sublimity turn out to be largely opposing: whereas the beautiful tends to the small, the smooth, the various, the delicate, the clear, and the bright, the sublime tends to the great, the uniform, the powerful, the obscure, and the somber. Hence Burke concludes that:
[t]he ideas of the sublime and the beautiful stand on foundations so different, that it is hard … to think of reconciling them in the same subject, without considerably lessening the effect of the one or the other upon the passions. (Burke 1990, 103)
The impact of Burke's aesthetic dualism was immediate. Before its appearance, the sublime could be ignored: there is almost no mention of it in Shaftesbury, Hutcheson, or Hume. Afterward it could not be: indeed the major theorists of the second half of the century—Reid, Alison, and Kant—all advance substantial theories of the sublime.
For example, Kant theorizes the sublime as "a feeling of the superiority of our own power of reason, as a supersensible faculty, over nature". Hannah Ginsborg says, in the Stanford Encyclopedia of Philosophy again:
Kant says that we consider nature as “dynamically sublime” when we consider it as “a power that has no dominion over us” (§28, 260). We have the feeling of the dynamically sublime when we experience nature as fearful while knowing ourselves to be in a position of safety and hence without in fact being afraid.
The connection with Burke is obvious.
To conclude, then: while it is true that sublime is not used in this way in everyday discourse, in philosophy (specifically in aesthetic theory) the sublime has certainly been connected with discomfort and pain.