CHLAMYDIA transmission this way?

So I found out that I tested positive for chlamydia! The doc gave me a one time antibiotic! I started the antibiotic on a Tuesday night! Saturday morning, I remember (this is GROSS!! Please don’t judge!) my vagina was itching & so i scratched it without a thought really! I don’t remember any fluid or anything being under my nail or on my fingers! So a little while later, I picked my baby up & my finger touched his hand!!! After I touched his hand, I was like “oh no!!” I don’t remember if he put his hand in his mouth afterwards or not or rubbed his eye or anything! I should’ve immediately washed his hand! Bc I didn’t wash mine after that quick little itch! I usually always wash my hands! Could chlamydia be transferred to my baby this way?? I am so nervous!!!!