We've been in tick country and diligently check the dogs several times a day. Last night I bathed both dogs and did the tick check. None. Today was a driving day and at one point DH had Butterscot...
I too live in major tick country, I get my dog vaccinated for lymes as well as use a topical protector on her. The red patch is very common and I don't think I would worry about it. Keep an eye on it though and if it's still red in a few days, then the advice prior was good, get it checked out.