It's also likely that during your pregnancies, you were tested for gonorrhea and chlamydia, though that's not as standard as it should be.
However, if you had passed an STD to your child during birth, your baby would have been very ill. Gonorrhea and chlamydia can infected a newborn's eyes, give them pneumonia, among other things. If you have herpes, the only dangers would be if you were infected during the third trimester or had an outbreak during birth - both of which you'd know by now.
A baby born with an STD isn't something you or your doctors would miss. You can stop worrying. :)