HELP! Sunscreen, allergy?

I went to the dermatologist and bought a sunscreen, which is working miracles for my face. One of the ladies suggested maybe I should do it on my hands just to protect it from uv damage because she does it as well. So I was like you know what why not so I just applied it on my hands and palms, but a few days later, I am not sure what happened, but my skin started flaking. It started turning darker only on my hands where I applied it. It’s dry red and it’s getting darker brown. is it an allergic reaction? If it is, I’m not sure why because my face is completely fine. It’s actually getting better on my face. does the hyper pigmentation go away? Because my hand are a shade darker than the rest of my arms.