I have a small lump about the size of a grain of rice on the side of my left wrist beneath my thumb. Its not visible, can be moved a little, and hurts?

Possibilities. One common condition that causes lumps on the wrist are ganglion cysts. These are formed by the fluid in your joints, synovial fluid, that normally lubricates the joints but have leaked out forming a small cyst in the nearby soft tissue. They are almost always harmless but can be treated if they become large and painful.