Second baby with clomid

Anne 💙💙💙 • Mom to 3 boys. August 2015, December 2016, December 2018
I had my son in August. Conceived in my 3rd round of clomid. He is now 4 1/2 months old. We would like to have a second child. I'm nervous about asking my doctor for clomid again so soon after birth. I did ovulation tests over the last two months and I never got even close to a positive test. Anyone know if doctors will even give clomid when not much time has passed since a baby?