Did your baby ever get food allergies from Baby foods?

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I started letting my daughter eat baby foods. (bananas, apples, carrots jar) and rice cereal. She started getting a rash on her butt and under her stomach. She has a runny nose for 2 days. Those are signs of food allergies. But it could also be because she has a diaper rash. And the runny nose could be from getting cold at night. I asked the Dr. and he said it looks like a diaper rash. But i want to be certain its not food allergies. Do any of you mothers have any helpful tips?