I have a swollen sore spot on the top of my wrist. It hurts and limits my hand and finger movement. Is this a tumor?

Could be, but.... It is most likely a ganglion cyst--a benign cyst that originates from (usually) the wrist joint and is filled with joint fluid. To be sure, see a hand surgeon. These can be removed, but they have a fairly high recurrence rate and their removal may not relieve the pain. Get it checked.
Yes, possibly. Any abnormal growth in your body is a tumor. If it is growing, causes discomfort or interferes with activity, as you are describing, it is time to see your doctor.