where exactly are you sore? near the bottom of your thumb maybe?

6 weeks for a sprained wrist seems very long to be honest. sometimes in the wrist there can be small fractures that dont show up on xray initially, it takes maybe two weeks to see them on a film. are you to go back to the doctor for a review? this is rare enough however.

you should book in with a physio. they can guide you as to when you can stop wearing the splint. for me, it would only be until the acute very painful phase is over and once you can start to move the wrist without a lot of pain you would start range of movement exercises and strengthening etc. keeping the wrist in the splint for a prolonged time would only lead to weakness, stiffness and maybe reluctance to move it.