Many companies are asking for code that you have worked on, and many of them ask for a GitHub profile. All my code is written for a company, and I feel I cannot publicize that. I have no projects, yet
Ruh-roh. You only code at work? That's... unusual.
Not too clear on OP's situation but it may not be as unusual. I'm a college graduate and I've seen a fair number of young interns who've had their first hack at coding at work. Not everyone has time to do personal projects...very dependent on personal situations.