Your situation is concerning. I would recommend that you see a dermatologist
(a skin specialist) at the earliest possible to have this evaluated. There are many causes of your condition, some of which are minor and some of which are more serious.
The first possible cause is xerosis, or dry skin. This can cause peeling, itching and cracking of the skin, however is rarely as severe as you describe. Many hydrating creams are helpful for this. However, given is severity, it is unlikely to be solely the cause.
Another possibility is contact dermatitis. Many people are allergic to the skin lotions out there, specifically the ones with fragrances. In addition, neosporin is something that people are also often allergic to. It may be the you started with some dry skin, and now the lotions are causing a severe contact dermatitis. I would try stopping all lotions except for maybe a fragrance free hydrating cream (like Eucerin).
Another possibility is this is infected. Both bacterial and fungal infections can cause this.
There are also primary skin problems like psoriasis
that can appear like this.
Finally, the most concerning is a reaction to your medicine. Steven Johnson Syndrome can occur as a reaction to medications that can be severe and appear like this.
I would recommend a dermatologist.