That looks similar to my husbands who has a bad case of it on hands & fingers. His used to be much, much worse. It's really hard to tell b/c dh really can take so many forms as is evidenced by the sticky at the top of the dh forum. At any rate, you really need to get tested since your sister has celiac & it is a genetic disease. Odds are...... Plus people with celiac disease tend to have skin issues & rashes of numerous kinds/types AND we tend to have allergies. Allergies can get much better & some even go away once we go gluten free. Just FYI.
Please make sure your sister checks out the Newbie 101 on this board.
It's not just as simple as "thinking" you are gluten free. There are issues with kitchen items and things you might think are gluten free but are not such as Quaker oats. Celiacs have to have certified gluten free oats, grown in dedicated fields, harvested on clean equipment & processed in clean facilities.