So first, you don't know it's herpes until a doctor cultures it and that comes back as herpes.
If it is herpes, the skin on your fingers is too thick to infect. Since you mention no cuts, and if you had cuts, you'd have mentioned them, you don't have to worry about your thumb.
Get yourself to a doctor - even an urgent care or walk in clinic is fine - and ask them to do a culture on you to make sure it's herpes. Don't let them visually diagnose you. It could be an allergy, impetigo, chelitis, or a host of other things. (And don't let a doctor tell you impetigo only happens to kids - I had it in my 20s.)
Let us know what the doctor says.