Could a cut on my finger that happened five hours ago still be making me dizzy? it wasn't too deep, but i did feel weak afterwards, and started feeling dizzy about an hour later.

Dizzy: Yes, it could make you dizzy, by something called the vasovagal response. Many people when they are hurt, nervous, or a combo of both, feel lightheaded due to a lowering of their blood pressure. I doubt you bled that much from your finger to have your blood pressure be low due to a loss of blood. Lie down and put a cool towel on your head, raise your feet up too, to get blood back to your head.