I'm sure other people have said this, but you need talk to your doctor. Usually something like the placenta sitting too low can be a worry for placentia-previa. But if your doctor told you not to worry, he probably meant that there isn't anything to worry about yet and he was just making sure with a careful ultrasound that everything is okay. If they are being so careful, you will know if a problem is brewing.
The reason I tell you to talk to your doctor is because you need to develop a relationship of trust with him. You need to make sure that he is listening to you and that he will answer all of your questions until you understand what he is saying. You also need to make sure that you ask as many questions as you can. Getting online and asking strangers who are not medical professionals what might happen in your situation is just going to make you nervous, confused, or both. Talk to your doctor about any health concerns that you have, even if they seem silly. You will be grateful to have a real medical explanation that you can understand, and he will be grateful that you aren't asking a bunch of strangers for advice that might be bad for you. Your health and the health of your baby is your first concern, so never be afraid to ask as many questions as you can. Good luck and congratulations.