Hi there!
Well, it first needs to be determines as to what is causing the inability to bend the finger. All fractures need to be seen by an orthopedician and evaluated for nerve/ muscle injuries as well. The cause of disability in your case could be muscle stiffness, mal/ non-union, nerve/ muscle injuries etc. It is best advised to see an orthopedician to determine the exact cause. A few tests like routine blood tests, imaging studies like x-rays. MRI, EMG, nerve conduction studies may be required for the same. After a caused is determined, it can be managed accordingly. If everything else appears to be fine, physiotherapy may be initiated to help with the stiffness.
Hope this helps.
Take care!
You need to go see an orthopedic surgeon. You probably need some physical therapy to get your finger moving again if you've been wearing that brace for a month and another xray to make sure that it is healing ok!