Hi, Welcome to Healthcaremagic!
1. Cold sores = herpes virus infection
2. Herpes on lips = herpes labialis = caused by herpes virus- 1
3. Herpes on genitalia = genital herpes
= caused by herpes virus-2
I hope this explains your query [note- HSV- 2 can also cause lip infection
Now, I suggest you to consult a dermatologist
for proper treatment. Good luck.