There's a tiny red spot on my gums in the wisdom tooth area, though I already took it out. It really hurts in that area, what could be wrong?

Get checked. get checked by a dentist, rule out unresolved infection in the bone associated with the extracted wisdom tooth, or perhaps infection from an adjacent tooth draining to the extraction site. Alternatively, it could be either bone from the extraction site or even tooth structure that fractured during the extraction.