My 10 Year Old Scratched Her Mole at Her Lower Back Accidentally, Now Its Swollen and Seems to Be Infected, What Should I Do?

Retinols and/or retinoids will typically have no impact on mole removal.  The exception is if the surgeon uses a laser in conjunction to mole removal.  Some ablative lasers are best used in absence of a retinoid/retinol.

If you desire removal, a full thickness excision with scar improvement techniques would suffice in the treatment. Raffy Karamanoukian Los Angeles

For a mole on this area of the nose, I would recommend a shave excision method.  If need be to achieve better contour, a laser ablation can be performed immediately after the shave.    

I would highly encourage you to see a plastic surgeon or dermatologist to have the lesion evaluated and most likely biopsied.