how to treat persistent rash on 11 month old

My baby has been dealing with skin issues for about a month now. First she had a sinus infection and ear infection, accompanied by a full body skin colored rash of very tiny bumps, on her torso arms and legs. She got antibiotics for the ear and sinus infection, and the skin colored bumps disappeared, but was instead replaced by red bumps in her armpits and groin, and back, spreading lightly to her tummy and arms. I used to moisturize her with coconut oil, but when the red bumps appeared i thought maybe she needed something stronger for the cold weather. I got her an aveeno oatmeal lotion. It hasnt gotten worse, but it hasnt gotten better either. She isnt sick, no fever, eating, goingn to the bathroom as normal, her usual energetic loud self. The past two nights shes been waking up and itching, not wanting to sleep. Idk how to fix it and I hate seeing her skin in pain. Unsure if I need to take her back in to the ped or do a topical solution. Any insights or advice please!