Zoloft prescribed

I was prescribed Zoloft for postpartum depression. I have a 2yo & a 1 month old. I'm home with them by myself 9 times out of 10 & I'm reading the side effects which say may cause drowsiness. I asked the dr before getting them prescribed will they make me sleepy she said no. I'm afraid to take them b/c I don't want to be falling asleep on them two & not waking up or ring too drowsy to where I can't tend to my one month old causing me to drop him or something crazy like that. Is anyone on this medication? Does it really make you sleepy? Any advice please?