A history will help diagnose this rash
If the lesions come and go within a 24-hour period, the likely diagnosis is urticaria. If they are slowly expanding, then consider an annular erythema. If the lesions are fixed, the possible diagnoses include sarcoidosis, granuloma annulare and subacute lupus erythematosus.
The rings might suggest a tinea infection but there are no surface scales, virtually ruling out that diagnosis.
This rash has been diagnosed on skin biopsy as a Jessner’s lymphocytic infiltrate.