You are incorrect about this. Worst case and Big O are independent of one another. The O, Ω, Θ, etc... are about describing bounds where O(f) is used for the set of asymptotic upper bounds on f, Ω(f) is the set of asymptotic lower bounds on f, and Θ(f) is the intersection of O(f) and Ω(f).

Typically f is used to describe space or time complexity of an algorithm, but it can be used for any function that maps positive integers to the non-negative real numbers.

You can make any combination of best case/worst case/average case with O, Ω, Θ. In fact, you can even consider other cases as well such as amortized cases, 90th percentile cases, any case you want to investigate that can be defined as a function from positive integers to non-negative real numbers can be classified as having an asymptotic upper bound, lower bound, or tight bound.