If I work on a holiday can I take another day off to make up for it?

Assuming you work in a private business (not the government) the answer completely depends on your employer's policies. An employee handbook should detail the time-off procedures, and it seems logical that if you're entitled to paid time off for a holiday, but end up having to work nonetheless, your employer would make it up to you, at least financially, on another occasion. You should speak, or write, to your manager or supervisor about the issue if the answer, and a solution, isn't obvious. Otherwise, consider contacting BOLI.