I had the same exact problem..
I took a fall 3 years ago on a rail (first time hitting rails)
knocked 2 teeth out, broke my thumb and basically tore through the ligament that skiers thumb is associated with. When the ligament tore it also pulled a piece of bone off and it floating around in my thumb somewhere haha
went to the docs and he didnt even take a close up image of it, basically just took my thumb bent it and told me i need surgery that following friday. Well 2 days before the surgery, swelling went down, pain was subsiding and i was gaining movement in my thumb. Got a second opinion, kept it casted for another 2 weeks and it healed up. Doc said i may have problems later and may have to get it fixed though.
Every now and again i have some pain in my thumb when i fall but it goes away within a day. I dont use straps on my poles, when im not in park I do.