Autoinoculation is only a concern with first infection when an immune response has not yet been established. It is not a concern after that because the virus is already in that nerve group.
You did NOT transmit this to your grandchild. If you did, symptoms would appear within 2-10 days but I really really don’t think you did.
I would agree with your doctor that there is no point in typing this virus – it is definitely behaving like HSV 1.
Are you really certain that the thing on your nose was a herpes outbreak?