Will cortaid (hydrocortisone) cure a ringworm rash or do I have to use an antifungal cream?

It can make it worse. The application of Cortaid or similar steroid creams can actually aggravate a true ringworm. Topical anti=fungal agents like otc tinactin (tolnaftate) are more likely to eliminate the fungus.
DO NOT USE! Using a steroid cream on a fungal infection is like pouring gasoline on an open fire. It will become redder, angrier, itchier, larger and "worser". An appropriate antifungal cream is what is need if indeed on oral medication may be needed. This is true especially with fungal infecitons on the scalp. Using for 2-4 weeks is usually needed completely cure the infection. If in doubt, see a doctor.