I have a bump in the palm of my hand and when I press down on it, it hurts. Is this a tumor?

Definition of tumor . Any bump bigger than 1cm, very unlikely to be malignant unless it's skin cancer.
Possibly. Lumps and bumps are very common in the hands. The most common masses in the hands include ganglions, giant cell tumors, and epidermal inclusion cysts. These are all benign, but they can also cause pain. A hand surgery consultation is strongly recommended to rule out masses of a more dangerous variety.