I didn't get my babys heart beat untill 11 weeks my doc was originally just going to try to hear it at 12 weeks but decided to do it sooner . I wanted to change docters at first too but I didn't$
With the two kids I have I heard both of their heartbeats at 10 weeks. But I am pretty thin (5'7 103 lbs) I think they've told me that normally on a normal sized person it's more like 12 weeks and more time for more "layers". My Dr. that I'm going to now (we moved from MD to WV) did a confirming scan at my initial appt. at 6 weeks that showed two sacs, two babies and two heartbeats, and then he zoomed in on each baby to see their heartrates. I've had two more u/s since then and have another one in a week for the anatomy scan so they can see boys/girls and measure limbs, head etc. I got the extra 2 u/s only because of having twins. Now with my other two kids that I had in MD my Dr. would normally only do an u/s at 16-18 weeks for the anatomy scan unless there was a problem or a history of problems. And they were really good. Another thing is is that with the MD Dr. they didn't have an u/s machine in office but my WV Dr. does so that makes a difference too. So they may not be totally off. When's your next appt? But if you don't feel comfortable maybe start looking because you definately need someone you can trust for pregnancy.
You should typically be able to hear the heartbeat at around 8 weeks. I did not have my first sonogram until I was 13 weeks pregnant. I am 26 weeks now. You said you have no insurance, but then went on to say that you have medical insurance so I am a little confused. Now days most doctors give two sonograms, even though my medicaid only is supposed to cover only one, I still recieved two at no charge to me. One sonogram is to take measurments and give a due date, and the other is for gender and to take more measurements. At every appointment the doctor should get out their little portable doplar thing and check only the heartbeat. Atleast thats how it has been for me. At your next obgyn appointment, if they do not do a sonogram or atleast check for the heartbeat, I would ask them bout it. Checking the heartbeat is an important part of checking on the baby as your pregnancy progresses so they will hopefully do it at your next appointment! Good Luck! & I wouldnt worry about changing doctors unless they continue to not check the heartbeat.