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> exactly correct in physics, and quantum mechanics is one of them, alongside Relativity

what about gravity? If we don't know the correct account of that, how can we know those are exactly correct?

First, we know for certain that pretty much everything other than gravity is described by quantum theories. It's almost an impossibility to merge quantum theories with non-quantum theories in a logically coherent manner, so either there exists a quantum theory of gravity (which we just haven't discovered yet), or the rest of physics is not really quantum mechanical. But there's a strong theorem (Bell's inequality) that rules out non-quantum explanations of experiments we can conduct in the lab, unless you invoke truly exotic explanations that are much weirder and implausible than quantum mechanics.

So we really are stuck with quantum mechanics, and there must be a quantum theory of gravity. In fact, there are actually quantum theories of gravity (including String Theory), but we don't know whether they're the correct theory that describes our universe.

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