An orthopedic specialist. They deal in bones.
Too many people get all nervous about hydro-cortisone treatments.
They are safe and keep the inflammation down so the tissues can heal.
Aspirin, which has fallen out of mode, is really a very good drug to use too. It also reduces the inflammation a lot better than most NSAIDs.
One thing people never consider is application of a methyl salicylic product on the finger itself. That is a closely-related drug to aspirin and it can help with the inflammation and let healing complete a lot better. There are the sports pain relieving products that smell like wintergreen and they are usually what you want.
NOTE from the Medical Wiki: Salicylic acid is known for its ability to ease aches and pains and reduce fevers. These medicinal properties, particularly fever relief, have been known since ancient times, and it was used as an anti-inflammatory drug.
In modern medicine, salicylic acid and its derivatives are used as constituents of some rubefacient products. For example, methyl salicylate is used as a liniment to soothe joint and muscle pain, and choline salicylate is used topically to relieve the pain of aphthous ulcers.