What should I do about my wrist?

Today during PE, I was running backwards (for a warmup) and I tripped and I put my hands out, landing with my palms on the floor behind me. It got pretty swollen and hurt quite a bit. I went to the nurse and got some ice, which I had on for about 2 hours. It has been about 7 hours and it doesn't really hurt when it is still but it hurts especially when I move it back, when I move it forward, and sideways. It hurts when I put pressure on it or pick up something really light. It also hurts when I make a fist. Now it is bruised (i think, there is some veins that it might be also, but i doubt it). It hurts right below my wrist everywhere when I apply quite a bit of pressure. Should I go to the hospital? What might it be? Please don't just say yes or no, and anything that I should notice that would be bad or worried about? Any help you can give me. Please answer soon and quickly. Thanks.It is also not slight movements. I have to really move it forward for it to hurt and not that far back for it to hurt, but it doesn't take much to make it hurt when I move it sideways. It also doesn't hurt that much, but it still does.