Nail Trauma Paronychia
By the looks of the photo, it is a paronychia, an infection around a fingernail or toenail. This infection is probably the result of repeated trauma as her foot struck the ground and the top of the nail struck her shoe. A little bacteria (staphylococcus) was able to take hold in the skin as it broke through the protective cuticle.
Because she is healthy, without diabetes or other immune problems, I advised frequent hot water soaks to increase blood flow and (hopefully) promote natural immune healing. If the swelling worsens or pus appears, it can be cured by excising it to drain. Topical antibiotics are of no use and rarely are oral antibiotics needed unless the infection is worsening.