"I'm scared" and "I'm frightened" are interchangeable. I can't think of any difference between them. Both are standard English.
"I'm freaking out" is colloquial English. It became common the in 1960s to describe the behavior of people who had taken LSD and were on a "bad trip." It suggests extreme excitement--including fear, but not necessarily fear--together with hallucinations, and bizarre behavior such as yelling and making noise. It suggests a reaction to psychedelic drugs.
Nowadays it's used as exaggeration of something milder. For example, someone at work yells a bad word. Heads turn. Someone says "what's wrong with _him?_" "Oh, he's freaking out because they just got another shipment of the wrong parts." "Yes, it's enough to drive anybody crazy."