This is an extremely common snowboarding injury. It could be something as simple as a sprain or it could be a more serious condition called snowboarder's ankle which is a fracture of the lateral process of the talus. The lateral process of the talus is a triangular protrusion of bone that sticks out from the outside of your talus. The talus is the middle bone in your ankle that sits on top of your heel bone. You should definitely get this checked out by a doctor asap. X-rays are notoriously unreliable for this type of fracture so if the x-ray doesn't show anything then you should insist on an mri.
Don't just brush it off as a sprain and assume it's no big deal. I made that mistake 6 years ago and I regret it to this day. I waited two months after the x-ray came up negative before I went for the mri and it turned out I had been walking around on a fractured ankle for two months. I had to get surgery to put the piece of bone back into the proper position with screws and they had to dig around in there to remove excess bone fragments from the subtalar joint. No fun at all trust me. Get it taken care of now before it gets worse.
If it is just a sprain then congrats you lucked out but you might still have a bruised talus in which case it will take longer to heal than your average sprain, probably more like a month rather than just two weeks. Like I said these injuries are extremely common and they happen to the best of us. Shaun White chipped his talus last winter in his private Red Bull halfpipe while tricking into a foam pit, so even landing into what you would assume is a nice cushioned foam pit and he still chipped that bone a little. He couldn't skateboard all summer long but luckily he got it taken care of right away and he was good to go for the 2010 olympics. We all saw how well he performed in the olympics so keep your eye on the big picture. Don't be so eager to keep on riding now at the cost of permanently damaging your ankle and jeaopardizing your chances of lots more riding in the future.
As far as boot tightness and boot sizing goes, yeah a tighter boot, smaller boot, tighter binding will certainly help but it's no guarantee. Anything can happen out there. The twisting and bending and all the kinetic energy involved when you're coming down from a big air, you just don't know. Unless you have a hardshell ski boot on, there's a good chance of injury, especially if you stick the tip and do the head over heels thing. All a properly fitted snowboard boot is going to do is maybe take an injury that could have been a break and leave you with only a sprain or bruised bone instead. Even the stiffest soft snowboard boot is not very stiff or supportive compared to a hard shell ski boot.
I recently injured my ankle again on a cartwheeled landing in the backcountry, again a very soft deep pow landing but that doesn't always matter. I am getting the mri done on Monday. I am not even bothering with the x-ray because they are useless for this type of injury. You have to know for sure what you're dealing with so you will know your next move.