I have been having front upper left chest pain and dizziness. I have family history of heart problems. My mom has a bad heart valve and an aortic aneurysm. I have no health insurance currently. What would be your best advice?

A free health clinic. If you can't afford to see a cardiologist there are a number of places where you can be seen for very little. You may have to show that you can't afford to pay.
Chest pain. Better to get checked with a family history of heart problems. Ask your local hospital or physicians to help you out in setting up a payment plans.