Painless non itchy rashes since 15 days.

Hi , i am a mother of 1 year old baby boy, my baby is having on and off red rashes ( painless and non itchy) since 15 days, no fever or any other symptoms associated. We did consulted a doctor online as well as in person and he told to give atarax drops and lacto calamine lotionas it may be contact dermatitis. After the giving atarx drops for 2 days the rashes became very few 2-3 but again after 3-4 days rashes have reappeared without any symptom. What should i do, should we go for some blood test or any other test to check what is causing these, i'm really worried for my baby and its very scary to see such rashes on his body, earlier the rashes were appearing on legs mostly, now they are seen on hands and stomach as well. Please help, a worried mom here