Bottom line: DON'T GO HOME without a thorough evaluation. Second, ask for "serial" cardiac enzymes that are repeated two or three times, every four to six hours. Third, ask for a repeat ECG to compare to the one you got initially.
Finally, ask for a definitive test before discharge. This may be a treadmill stress test with echocardiography (no radiation) or nuclear imaging (radiation). In some ERs, the CACS or the advanced coronary CT angiogram may be available. If you're not severely allergic to iodine dye, this is by far the most accurate way to be sure your arteries are clean. If they aren't clean, a cardiologist will have to evaluate your status, but you'll know the score and -- most importantly -- be alive.
Ask for advanced labs
I've had 30-plus years of training and practice, so I can tell you that you'll probably have the same lab tests at an annual physical now as you would've in the 1970s. This isn't just outdated, it's unacceptable -- there have been major advances in laboratory testing in the past 40 years, believe it or not. I suggest asking for the following tests: