The great news in this situation is that the person who has HSV 2 almost never acquires HSV 1 subsequently. First, there’s that, and second, I doubt very much that you acquired HS 1 from the kind of contact that you had with your visitor. Third, since your symptoms showed up a month after the contact, if you have HSV 1, then it wasn’t from that contact. Fourth, it doesn’t really sound like a cold sore to me, from the way that you describe it.
But the first point of people with HSV 2 not getting HSV 1 is the most important.
You did NOT infect your daughter.