Sudden hard lump over big toe joint. Lots of pain. Can't wear sneaker. Ball of foot/ankle/big toe pain. Hard time walking. What could it be?

Possible mass. It is possible that you have a soft tissue mass over your big toe joint. If there is a history of trauma to the area, it could be a ganlionic cyst. An x-ray is needed to rule out any changes in the joint that could contribute to this condition.
Many. Possibilities bursa, bone spurring really needs to be seen and x-ray to make good diagnosis and treatment.
Big toe. The suddenness is a cause for concern. Without an xray to help with an evaluation , it is very difficult to state definitively what may be going on. Seek the help of a podiatrist - good luck .