Need Advice About an F - First Time Poster on College Confidential

I am a sophomore in a public university and unfortunately I had gotten an F in one of my core classes. Although the class was not worth many credits (2 specfically),

I am worried about it affecting my chances in transferring out of the public university and my chances in applying to graduate schools, although I have a moderately high GPA (3.68).

My question is, what should I do now? And is this F simply going to be hanging around in my GPA/ Transcript throughout my academic career?

BTW if I posted this in the wrong section, sorry still new to this.