Birth certificate for newborn

when I was in the hospital I signed a birth certificate form but my baby is now a month & im not sure if I’m supposed to send in the payment or what because I went as far going on the website & ordering a birth certificate but I shouldn’t have to if I signed up for one at the hospital so I’m a bit confused & I wanted to know how y’all got yours or if you haven’t yet also I made a mistake on my baby’s name so I’m trying to hurry & clear this up before it’s to late because I already have her SS card which I’m going to make a change to so any info would be great btw I live in the dmv