Sounds like a hyperextension, if you can walk it's not likely broken but if it still hurts it's likely sprained. If it's still painful I'd recommend not training on it, if you want to go to class it shouldn't be an issue but you will want to tape it to the toe next to it and don't be hard on it.
I can't judge how bad it is, but if it doesn't look good then rest for a few days, apply ice(10 minutes on, 10 off), and try to keep it elevated above your heart. If the injury lasts more then a a week or feels unbearable you should have it looked at.
Unlike what most people think avoid applying pressure to it as it will slow the blood flow so it won't heal as fast. If it's swollen avoid applying heat as it will likely have a negative effect.
It might seem like it's just a toe but your whole body is important, take care of it today so you can still train tomorrow.
Also it sounds like when you kick your toes are what lands. Toes are fine is you're doing a push kick but if you going for power you should use your heel, the toes are fragile.