I cut my finger quite badly earlier, it had stopped bleeding but am experiencing fairly painful throbbing. my finger is red and warm to touch.

Inflammation: from injury, may be associated with a cut...and throbbing may accompany an injury, but infection, hot red warm can be a significant problem for finger lacerations, especially if the cut was dirt y or countermined with meat, food , wood most anything, if this continues seek medical attention . Even if it is for what is called a "bad" cut as a bad cut