Iunderstand your urge to try the Antibiotic topical that is being suggested by your primary care physician. If you feel strongly about it, go ahead and try it for a couple of weeks. If it doesn't help, you can always get back on the track with leaving them alone. You should also consider those of us on the forum are not doctors and our opinions are just that - opinions based on individual experiences. With that said, I still strongly encourage you not to peel off the flakes. Also, I tried a prescription strength Antibiotic ointment and it did not help. I don't remember it doing any harm, but this was when things were at their worst, so I would not have known if there was harm being done.
At their worst, I'd say 2/3 of my lower and upper lip were affected. I'm not sure how to describe how large the crusts were, but they were close to the size of the crusts in your picture.
Please let us know what your dermatologist suggests.