When I was pregnant with our daughter I had the screening done because of my "advanced maternal age" which already put me at a higher risk for Downs. They did blood work and also an ultrasound to measure the fluid at the back of the baby's neck. The ultrasound was fine, but the bloodwork showed a 1in 60 chance of Downs. I was really scared. I've worked off and on with people with Downs for about 25 years so I knew what we could expect. I knew we would be fine and that the hardest part would be coming to accept what would be normal. We chose not to do an amnio because there is a slight risk of miscarriage and I had just had a miscarriage scare the week before. I couldn't handle the stress of that. Our daughter will be 3 this month. She was not born with Downs. When I was pregnant with our son we chose not to have the screening done. The stress wasn't worth it for us. We knew that knowing wouldn't change anything. Our son will be 1 next month. He was also born without Downs.
I know it will be hard not to worry. One of the things that helped me mist was something that the genetics specialist told me. She said that having a 1in 60 chance meant that if I had 60 babies, maybe one of them would have Downs. That made the odds seem not so scary.
There are some great books out there about babies with Downs. Look at the Down Syndrome Society web page. They have tons of resources.
Talk to a pharmacist about what over the counter sleep aids you can take. They can also let you know what precriptions would be safe for you to take. My husband is a pharmacist and I swear he knows more about what is ok than the doctors do. A pharmacist can at least give you an idea of specific meds you can ask your doctor about. If your doctor isn't taking you seriously find a new one. You will be under enough stress without having an uncaring doctor as well.
Try not to worry. No matter what happens you will have a beautiful child that you will love beyond belief. It may not seem like it now, but this will make you a stronger person and a better mom. You will be in my thoughts and prayers.