There is no requirement under South Carolina law for an employer to provide employees with breaks or a lunch period.
Federal law does not require lunch or coffee breaks.
In most states, breaks are required by law. The employer has to, by law, enforce that employees take those breaks. If they fail to do so, it opens them up to very expensive lawsuits. I recall a decade or two back, The Gap has a massive settlement in the state of California over employees working through breaks.
If HR won't help you, go to your local labor board and report them. And if you do go to your local labor board, talk to a lawyer and let them know what's going on. Also, try and take your 30-minute breaks to show that you're following the law or at least trying to. Plus, it'll give you more evidence against your boss.
Yes, you can bring a legal claim associated with the employer not providing you with a reasonable opportunity to take your meal or rest periods.
California Labor Code 512 is the state statute that gives certain employees the right to an unpaid meal break during their shift. The law is meant to allow employees to have a rest during their workday. It is also meant to prevent employers from keeping employees on the clock for too long without a break.