What is the correct sentence "Got Pregnant" or "Became Pregnant"?

Both are correct. As others have pointed out, "became pregnant" is formal and "got pregnant" is more informal (though not always the case). There is also a slight nuance (subtle difference or shade in meaning) between the two: "Became pregnant" suggests or indicates that the woman has simply entered into a state of pregnancy, no more, no less. So practically speaking, it's a literal sense. "Got pregnant" can be used to suggest the woman became pregnant by accident.