No sonogram until 13 weeks?

So I went for what I thought would be my first sonogram. Instead it was 100 questions about my and my husband's medical history, a pap smear, and discussing blood test results. Needless to say, I cried alot because I wanted to see my baby. This turned out to be what I would consider a routine check up. They said that they would do the first sonogram in 4 weeks when they do the downs syndrome screening at 13 weeks. I've seen and heard about women getting sonograms as early as 5 weeks. I feel like for safety they should have done one but more than anything I feel like I was cheated. I'm considering just looking into doing one on my own or just switching doctors. Am i over reacting?