There are many possible causes of brownish spots on the legs and arms.
Some common causes include chronic eczema, lichen amyloidosis and venous stasis. If the rash is continuing to spread despite the use of moisturizers, it would be good for you to see your dermatologist for a closer and detailed examination and assessment to determine the exact diagnosis.
Sometimes, a skin biopsy may be require to confirm the diagnosis. Your doctor can then advise you on the most suitable treatment for your diagnosis.