About the "allergy to toothpaste" that you say you have ruled out.....
It isn't an allergy to toothpaste, it is an allergy or sensitivity to SLS (Sodium Lauryl Sulfate), which is an ingredient in most toothpastes and thousands of other products. So if you are still using mouthwash, or soap, or shampoo, or aftershave, or shaving cream, or Acne cream, or anything else that might touch your mouth or lips that has SLS in it, then just getting rid of the toothpaste might not have solved the problem.
If you want to check for SLS sensitivity, you will need to eliminate ALL products with SLS that might be coming in contact with your lips.
I know that SLS allergy can be a huge factor, because my lips are totally healed and normal since I eliminated all SLS. For me, that was the cause of my lip issues. It has been almost 2 months now, and my lips are totally normal for the first time in years. So I think eliminating all SLS for a month and seeing if it makes a difference is totally worth a try.