Hello and welcome to HCM, Skin lesions like red rash on body need to be examined before diagnosing the condition or starting with any treatment. It would be helpful if you could post the image of the lesion on different part of body. However, no response of the rashes to antibiotic ointment - neosporin indicates that the rash is not infectious in nature. Fungal infection can also cause round shaped rashes, however, fungal lesions are often itchy and the lesion is called ringworm. I am of the opinion that the rash is due to some primary skin lesion. There are number of skin diseases which manifest as red rashes like pityriasis, psoriasis, lichen planus etc. I suggest you to consult your dermatologist for clinical assessment and thus management. Thanks and take care Dr Shailja Puri