My puppy has a rash on tummy and leg/arm pits?

My poor little Lilly. She will be 3 months tomorrow. Over the past about 5 days she has developed a rash on her tummy. It goes across her whole belly and is all red with little red spots and is particularly bad where her belly meets her arms and legs. Some days it has been worse then others because there were times when we thought it was going away but has yet to do so. We have not changed her diet which consists of authority large breed puppy food - bully sticks and bones. She does go out into the grass every day and her and her sister play all the time - the rash has not affected her eating, drinking, or personality in any way. We did take her to the vet the other day for another reason in which she needed an antibiotic, the vet gave us the option to do a skin scraping but he didn't make it seem like it was anything serious so we did not do it because we were already spending quite a bit that day. I have been giving her half a benedryl which he recommended to help her itchiness but I haven't noticed it helping much. I would like some suggestions as to what this could be and how to treat it, We are going on a last minute road trip this afternoon and I want to be prepared and want to be able to do whats best for princess Lillian.