Your friction burn has almost healed, except for the central portion, and that is causing you worry.
Well, it appears to me that you may be "over-treating" it, with daily scrub, neosporin use, and
band-aid application. This may be preventing and hindering the natural healing process.
Any wound in the body heals by formation of scar tissue. Cells migrate to the wounded area, and lay a new
meshwork of blood vessels, stromal connective tissue, and skin. The layer of skin laid by the healing tissue
is initially very fragile, and may consist of only one or a few layers of cells. This later matures to form
the fully healed natural skin.
If you scrub down your knee "sore" daily while taking a shower, you may actually be removing layers
of the healing skin tissue. This has lead to chronic "sore" formation.
If your knee is not infected, then it would be a good idea to just leave it alone. Do not scrub it vigorously,
although you may dab it with cool clean water containing a mild antiseptic. Do not apply ointments or band-aid
if it is not infected. Do not touch it needlessly. Avoid clothes rubbing on it. If you notice any pus,
discharge, or bleed, pl consult your doctor.
You have mentioned that you do not have any other medical issues. That is good, because minor wounds may take
a longer time to heal in patients with diabetes.