The medical name for your condition is cheilitis, roughly eczema of the lip. It's a sensitivity rarely triggered by something specific (toothpaste, lipstick, mouthwash
, etc.), so unless you're convinced of such a correlation, I wouldn't look too hard for one.
Try using over-the-counter hydrocortisone 1% ointment, along with a heavy moisturizer like Aquaphor. Used regularly, these will quiet down each outbreak. In between, no need to do much of anything.