A diagnosis cannot be made safely without examining the rash, but
purpura on the lower legs with burning and itch raises concern for cutaneous small-vessel vasculitis (also called leukocytoclastic or hypersensitivity vasculitis). It often causes purple, non-blanching spots or raised patches on the legs, and can cause burning, swelling, and itch.
DermNet’s overview describes this pattern.
Until assessed: avoid scratching and avoid starting steroid creams, antibiotics, or anti-inflammatory pain medicines on your own. Take photos in good light, note any new medicines, infection/sore throat, foods, creams, or exposures during the last 1-3 weeks, and bring that information to the visit.