From the symptoms it can be an insect or an arthropod bite. Did you have a history of any tick bite recently? In that case bull’s eye pattern rash of tick bite should be ruled out. Do not use any cosmetic products at the sites. You can apply some calamine lotion at the rash as it will help in soothing the skin. You can take some OTC oral antihistamine medications like Benadryl or Claritin and see if it helps.
For mild-moderate symptoms a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid (e.g. clobetasol propionate, fluocinonide). But they are available under prescription and should be taken only after consulting a dermatologist. Also then other possibilities like heat rash and parasthesia skin should be ruled out.
I hope it helps. Take care and regards.