I had my first ultra sound yesterday 4/2/2013 and measured 6 weeks and 4days pregnant and the fetus is 6mm.

The doctor did not see any heartbeat should I worry?

I really am stressed out.

Was the doctor worried?

You have to realize that at six weeks the fetus is no bigger then a pea, so it would be near impossible to detect a heartbeat unless extremely diligent. Call your doctor instead of stressing out. I am sure you are stressing for nothing and will have to learn to be well informed and ask questions when you see your doctor.

Was the ultrasound abdominal or transvaginal? As tickle said, at 6 weeks it's really early to be looking for a heartbeat. The earliest I have seen is 9 weeks.

Agree, I see no issue if you are just 6 week pregnant