I'm sorry you even spend any time worrying about this, because it's not necessary.
The absolute only way you'll ever give your child herpes is if you are having inappropriate sexual contact with him. Herpes is not spread by normal household contact, normal child care, etc. You would have to have direct unclothed, skin to skin, genital to genital with someone to transmit it, and I'm assuming you haven't done that with your child.
That said, you should take your son to the doctor. He could have a fungal infection like jock itch or yeast, and need treatment. Don't even tell the doctor you have herpes - it's unnecessary.
Good luck, and I hope he heals quickly.
You should read the Herpes Handbook at https://westoverheights.com/herpes/the-updated-herpes-handbook/ It's written by Terri Warren, one of the world's leading experts in herpes, and it's free. This should help with your peace of mind.