Can taking prednisone or topical steroids make a rash worse?

Yes. Yes, especially if the rash is caused by infection or if there is an allergy to the specific steroid preparation.
Absolutely! Oral and topical steroids are useful for inflammatory skin conditions like eczema. However, these medications can be harmful and make a rash worse if the rash is caused by an infection. This is most commonly seen when a steroid is applied to a fungal rash (like athlete's foot or jock itch or ring worm). These infections use steroids like gasoline on a fire and cause the rash to worsen quickly.