"I didn't get to say what I wanted to say" = there was no opportunity for me to say what I wanted to say. "I couldn't say what I wanted to say" = there was an opportunity for me to speak, but I was too shy, too scared, too embarrassed, too polite......

Yes, "I couldn't say what I wanted to say" is grammatically correct:) Yes, "I didn't get to say what I wanted to say" means you couldn't say what you wanted to say because you didn't have enough time, or someone didn't allow you, or something:) I hope it was useful:) Greetings!:)