There is one specific rare rash that could possibly indicate a severe bacterial infection. It involves red lesions that may be the size of a pin (petechial), or a larger hematoma.
When stretching the skin and pressing on that specific rash, it does not disappear, because it is actually a bleeding that has occurred under the skin.
Petechial rash is a one good reason to see a doctor as soon as possible. Other reasons are here.