I too have splits on my thumbs, just at the corner of the nail. Get them regularly when the weather is just above, or below freezing. And as you say, picking things up can be so difficult, and fastening buttons can be excruciatingly painful.
I wear gloves at work whenever I can, to try and prevent me from stubbing my thumbs (doesn't always work though) And I also use an advanced healing gel. But to be honest, I only get respite once the weather changes, and the temperature starts to rise.
Hope you can find something more suitable that works for you.