A red rash could be a symptom of a staph infection, although without examining you, noone can make that determination. Most commonly, staphylococcus infections will result in an abscess, boil, or folliculitis. Just a rash is more likely to be a streptococcus infection or another reaction, such as to a medication or an allergic reaction.
If you are concerned about a rash you have, please be evaluated by your physician.