At around 8 weeks of pregnancy, the body makes 5 extra pounds of blood. When this happens, the blood pressure can go up and the heart can pound. When laying down, the head can pound very hard. After a couple of weeks, the symptoms usually subside. Make sure that you are drinking plenty of fluids and eating well for you and your baby. Pregnancy is a drain on the woman's body, so make sure that you are taking enough calcium. If the woman does not take enough calcium, the body will rob the bones of the woman for the baby. This is a mistake I made and I now have osteopenia (low bone density). Enjoy your pregnancy! It is a very special time. Get as much sleep as you can now before the baby is here.
Have you ever fainted before you were pregnant? A lot of women faint for the first time during pregnancy. But since you seem to have ongoing dizziness and have fainted twice I'm really surprised you weren't evaluated a little better. I would march back in there and demand an ECG and a holter monitor. You might get lucky (well not really) and have a dizzy spell or faint while wearing the monitor and it can rule out any heart problems.
It isn't good for you to be scared right now. Tell the doctor how you feel and that you just want to rule out any heart issues.
Good luck and try not to worry, most people who faint are just fine.