Thanks. I feel better now.
Your daughter probably is going to catch HSV-1 someday; half the population gets it. It's nothing to worry much about.
Transmission of genital herpes rarely if ever occurs other than by sexual contact; there is no risk to your daughter from your HSV-2 infection. To be extra safe, she shouldn't sleep in your bed if or when you are having an outbreak, but otherwise don't worry about it. The children of parents with HSV-2 just about never get infected unless there is sexual abuse.
However, there is a risk from your oral HSV-1 infection. You can minimize it by avoiding kissing your daughter when you have a cold sore, and by using common sense hygiene, like frequent handwashing when you have outbreaks. Even better, keep an alcohol sanitizer gel (e.g., Purell) in dispensers all around the house and use them frequently when you have cold sores. Otherwise, don't worry about it. Towels etc proibably aren't a significant risk; it is direct contact by kissing or from your hands that carries most of the risk.
However, don't go crazy about this. These approaches aren't perfect, since you could have periods of asymptomatic outbreaks you don't know about it. As a parent, I believe you are making a big mistake to never kiss your daughter! Preventing oral herpes isn't worth foregoing the physical closeness that is a very important part of parenting. And avoiding lip kissing probably makes no difference; the risk probably is almost as great from kissing her cheeks, forehead, etc. Your daughter is probably going to get oral HSV-1 someday (up to half of all kids get it). You can reduce but not completely prevent her catching it from you, but you can do nothing at all to protect her from all the infected kids at day care or school, or by contact with relatives or other adults. Most infections are mild or entirely asymptomatic, so if and when it happens, she and you might never know it.
On top of all that, your risk of transmission of either HSV-2 or HSV-2 probably is reduced by taking Valtrex. In fact, it sounds possible that your recent problem was a pimple and not herpes at all.
Don't get me wrong: all things considered, it is better if people don't get oral herpes. But total prevention is impossible and most infections are mild or asymptomatic, therefore not worth losing sleep over. Just use common sense hygiene and avoid kissing your daughter when you have oral outbreaks. Nothing more is necessary or wise.
If you haven't discussed all this with your child's prediatrician, please do so. I'll bet s/he says pretty much the same thing.
Best wishes-- HHH, MD