Like MauiWowie said, if you're absolutely sure it's not broken then don't bother going to a doctor, at least not yet. They will only tell you what you already know, rest, ice, compression, elevation. I didn't realize your injury was so fresh and for some reason I thought you said you cartwheeled your landing. If you came down on it really hard but didn't bend or twist it in any unnatural way and you were able to keep on riding the rest of the day then it most likely isn't broken.
I had a similar incident happen last season in the smaller terrain park at my mountain. I went into the jump too hot, overshot the transition and landed hard in the flats. It was jarring for sure and I could feel the compressive forces, but I was ok in a couple of days. In the end I just tweaked my achilles a bit. You have to be careful in those little grom parks because if you're used to hitting the real park you might accidentally carry too much speed into the jump and overshoot the landing.
Anyway it's the tipping forward on your board and the wrenching of your ankle into an excessive bend that will really mess you up, like when you flip and come down hard on your tip or your tail and lean your body too far in that direction or when you cartwheel your landing and bend forward too much. If you didn't do either of those things then you are probably ok.
Give it a week or two and see how it's doing. I would say don't ride on it again for at least a few days, optimally about a week and see if it feels significantly better. Also keep in mind that even if it is just a small ligament tear, that could open you up to a bigger injury since the ligaments are now weakened and if you take another har fall and put similar forces on it, the ankle could bend further next time which could lead to more severe tearing, bone chipping, etc. So if you do get back out there soon, try to tone down your aggressiveness at first.
My most recent injury was two weeks ago and it still isn't feeling much better so that's why I scheduled an MRI. I am somewhat hypersensitive to this kind of thing after my experience 6 years ago when they misdiagnosed my break as a sprain. I don't think my ankle is broken or even chipped this time around, but I just want to be absolutely sure so I don't inadvertently make it worse.
That's where I'm coming from. Better to be safe than sorry. For a $25 copay at the doctor's office you will know for sure and you can treat it accordingly at that point.