Hard to tell exactly from your pics. Maybe it's also because I'm logging on through my phone. But it looks like a middle third fracture with some displacement. Unless there was a break in the skin with bone sticking out, or unless the ends of the bone are tenting up the skin significantly, I think most orthopedist would lean towards non - op mgmt. but I don't fix these for a living, so stick with the advice of those that do. The ends will most likely mend together. You'll have a slight deformity/bump where they stick together, but for most people I don't think that's reason enough for surgery. There's a saying: there's no condition so bad that surgery can't make it worse.
And yeah, you're supposed to wear the splint all the time. And you're supposed to be taking it easy on that arm (not moving it around) so that the ends mend together and you don't wind up with a non -union or delayed union.