It won't heal!!! (Pic)

I have anxiety and one of my ticks is picking at the skin on my thumbs and it's also been very dry and cold where I live. Anyway, the skin on the side of my thumb started to split on both sides. One side has healed, but one side just won't heal no matter what I do and every time it seems to be close to healing, something happens where it splits open again. I've been putting antibiotic cream and a bandaid on it at night, but it starts to hurt from being compressed so I take it off. I have no idea what else I can do.