Circular dry patch on my wrist more noticeable some days than others. i've noticed that when i put lotion it gets red and i feel a burning sensation.

The patch could be: eczema or atopic dermatitis, both due to very dry skin and perhaps allergies. As you suggest, dryness is the main culprit. It may burn because the skin is so dry that there are actually microscopic cuts/breaks in it which burn when chemicals applied. Many lotions have alcohols or acids (glycolic, azaelaic, lactic) that are irritating. Humidify, hydrate, use sensitive skin lotions/creams.