no, you didn't transmit your genital herpes to your child's eyes! It just isn't that easy to do in the first place. Also the virus is easily killed with soap and water so just washing your hands after using the toilet or touching yourself intimately like you probably already do, is all the precaution it takes.
your son has a cold. red eyes and irritation are a part of that. no reason to think herpes :)
grace
The virus really doesn't live long on your hands. But you would have had to had an outbreak or been shedding touched your genital area not cleaned your hands and wiped his eyes. If that didn't take place nothing to worry about it.
How were you diagnoised with HSV-2?
Have your son looked at for his eyes.