I recently developed a rash. What can I do to get rid of it quickly?

Hydrocortisone cream. Topical steroid creams quickly reduce the redness, itching, and inflammation from a rash. If the rash is weeping, then calamine lotion can be used to help dry it as well. Of course, if it turns out to be a fungus infection (ringworm), then Hydrocortisone would improve the itching, but not resolve the rash at all.
Depends. If it itches, a cortisone cream may help. If it is infected, then an anti-bacterial cream may help. See you doctor if you are uncertain.