I had an accident and fell resulting in cutting my middle finger ;requiring 6-8 stiches; my ring finger has been burning at the last joint to tip?

Likely nerve injury: Sounds like a nerve injury, which are common. Is the burning in the same finger that was cut? If so, you likely cut the nerve in the process. If not, you may have crushed the nerve at the same time you got the cut. Usually, these nerve injuries heal with time, but can take months. You should have your doctor take a look, however.