Can cortisone cream make a skin rash worse?

If you have a fungal rash, yes!! Fungi LOVE cortisone and will get much , much worse! See your Dr for a good diagnosis of your rash so you know what you are dealing with.

Or the rash could be an infection (like yeast) and cortisone would make that worse.

Yes it can . You may be having an allergic reaction to the cream. Try something different. You may want to contact your Dr if the rash gets any worse.