Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain Stye is caused due to Bacterial infection in the gland over the base of eyelashes and needs treatment with antibiotics Oral intake and topical application and warm packs over the stye..
While
cold sore is a Viral Infection and is caused by
HERPES SIMPLEX VIRUS 1 and it is totally different from stye as it is caused be Bacteria..
Cold sores are extremely contagious and needs to be treated will
antiviral Oral and topical therapy like
Acyclovir therapy..
Both are completely different conditions and needs different treatment and one cannot cause other..
For the lip sore first you should
consult a Dermatologist and get evaluated as a pus filled bump can also be Bacterial infection and you can get treated once the doctor diagnoses it correctly after clinical evaluation and laboratory investigations if needed..
Hope this information helps..
Thanks and regards..
Dr.Honey Nandwani Arora..