No. It will not work. Ring worm of the scalp, medically known as tinea capitis, is treated with oral anti fungal medication (usually griseofulvin) for 2-3 months. This is a prescription drug. I recommend seeing your doctor to confirm the diagnosis and to obtain the prescription. Topical therapy is not effective in the scalp.
Won't fix it. When the scalp is invaded by the germ of ringworm it gets into the root system of the hair, far too deep for superficial creams or lotions to kill it all. They can attack the exposed fungus, but the root associated germ just replaces what is affected by the creams. See your doc for proper diagnosis. This commonly takes a month or more of oral anti-fungal meds.
See doctor. Ringworm of the scalp can be difficult to treat without the help of a physician. See your doctor for the best treatment options, which may include an oral anti fungal agent.
See below. Biotin shampoo, still better, selsen shampoo will produce the desirable resolution of the condition.
Home remedies. Work in many cases, but on scalp, must be sure it does not get into child's eyes or burn the scalp. Antifungal cream (lamisil ultra / tinactin (tolnaftate) / etc.) best first choice. 1:6 dilution bleach:water often recommended; vinegar use; tea tree oil use; coal tar shampoo; etc. All are recommended with variable success. Check internet for this advice, see pediatrician for formal recommendation.