What is a good non medical relief for itching

Depends on what is causing it.

Too vague. Could be dermatitis, infection, poison ivy, bug bite etc. etc.

I use 1% cortisone cream for every conceivable itch. Of course that can be called 'medical.' Not sure what you mean by that term. Prescription cortisone creams just have a higher %.

Baking soda and water is a good alternative.
Old fashioned calamine lotion, the pink stuff (haven't seen it in years)?
Aloe vera liquid straight out of the leaves of the plant.