HVS1??? Toddler and infant

I have a 4 year old and 3 month old. They both just started at daycare because I had to return to work after my maternity leave. My son was in a public daycare for years before, and they are now in an in-home daycare that was highly recommended. This week I noticed what looked like just a red pimple by his lip. It never looked like a blister at any point, and it looked like it was going away the other day but then it’s looked like this for 2 days now (pic below, don’t mind the peanut butter on his face, he just ate).

His dad says it’s got to be HSV1 because he’s had cold sores like that before when he was a kid. I’m so upset it seems like he may have got it from this new daycare :( thankfully his baby sister is separated all day from the kids his age, but how do I protect her at home? I have my son wash his hands all the time at home, and we use hand sanitizer frequently inbetween. But he’s barely just turned 4 and doesn’t understand when we say not to kiss baby sister, or to not touch her face or hands, and he’ll run up and do it in a split second of us looking away. He just wants to love on her 🙁 has anyone had to deal with this or have any advice?? Is this contagious even when he doesn’t have a visible cold sore?