They way to many times to have an hsv1 oral outbreak and having puss would also imply its not herpes
I have an ocd and fear of cold sores so I feel like maybe could be causing an outbreak every week
Maybe stress could be causing the outbreaks every week
You might want to have one swabbed to confirm they are in fact herpes sores.
If you are having pus containing sores on your lip every other week, you need to be seen promptly by a medical professional for a proper work up. Odds are these are not herpes related but obviously there is something going on that needs to be dealt with!