“I said to myself.” This is an English nuance of the Hebrew text, which is more literally, “I spoke with (or “to”) my heart.”
“my heart has seen.” The phrase “has seen” is an idiom. To “see” something in this context has a broad meaning, including to experience and to obtain. Thus, the literal “has seen” seems to be a better choice than picking a more nuanced word that is narrower in scope.