It appears that you are having a new onset of dry scaly patches of skin. There are a number of possibilities for the etiology of the “white/pinkish blotches of dry, flaky skin.”. On the top of the list includes dermatologic conditions such as psoriasis, eczema, fungal infections, or vitamin deficiencies.
Psoriasis is a common noncontagious disease of autoimmune etiology. It is a result of an overgrowth of skin cells that result in plaques forming in discreet regions. Nailbeds are frequently affected and nail damage is often a symptom. Treatment is often with steroids or other immunomodulators.
Eczema is thought to be an allergic reaction of the skin to external allergens. It appears as dry, inflammed, and red patches of skin. Like psoriasis, treatment is either with steroids and immunomodulators.
Fungal infections such as ring worm can cause similar symptoms as you are describing. Ring worm is caused by dermatophyte fungi – typically Tinea corporis and can arise in red, dry, circular lesions on the skin. Usually, treatment is with a topical antifungal for 4-6 weeks can cure the fungal infection.
Lastly vitamin deficiencies can cause dermatologic problems. Specifically, deficiencies in vitamins A, B6, B12, C, D, E, as well as zinc can all manifest in skin lesions.
As it is nearly impossible to diagnose your condition without a physical exam and detailed history, the proper way to screen your condition is either visit your primary care physician or see a licensed dermatologist.