I agree with Wendy. I'd say 'fret about'. The most important difference is that 'fret' is less formal than 'worry'. You wouldn't use it in academic or business writing.

Also: Personally, I don’t use “fret over” very much. If I use “fret”... I would say “fret about”, much like “worry about”.

I think they are pretty similar, but in colloquial speech I rarely hear anyone use “fret over” in California. We usually just say “Don’t worry about it!” Or “no worries!”. I’ve never heard someone say that they are fretting over something before, but we say we are worried quite often. I’m not sure about their difference in formal speech.

I have never heard "fret over" and I was born and live in New York

Hola Alina: Soy Colombiano y tengo 33 años. Soy bailarín de Ritmos Latinos, Administrador de empresas y actualmente estudio una Maestría, pero mi nivel de inglés es bajo. Entonces, quiero practicarlo, o simplemente enseñar mi idioma español. También compartir experiencias, cultura, anécdotas y conocer personas de todo el mundo; Hacer amigos! Sí te interesa, podemos hablar por Skype, WhatsApp o Facebook y ayudarnos mutuamente.