My doctor didn't find any down syndrome markers in the ultrasound. does that guarantee my baby won't have down syndrome?

No. OB's combine the: results of an integrated screening test that includes specific blood tests in both the first & 2nd trimesters + the first trimester ultrasound to determine a single Down Syndrome risk rating. Only prenatal diagnostic tests of fetal genetic material for either Karyotype to determine # of chromosomes or Chromosomal Microarray to determine mutations in smaller gene sequences are definitive.