This may be a side effect from the flu vaccine itself.
Not sure what actual flu vaccine you were given but choosing one of them...
The fluvaval vaccine package insert states:
Adverse events described here are included because: a) they represent reactions which are known to occur following immunizations generally or influenza immunizations specifically; b) they are potentially serious; or c) the frequency of reporting.
Blood and Lymphatic System Disorders: Lymphadenopathy.
Eye Disorders: Conjunctivitis, eye pain, photophobia.
Gastrointestinal Disorders: Dysphagia, vomiting.
General Disorders and Administration Site Conditions: Chest pain, injection site inflammation, rigors, asthenia, injection site rash, influenza-like symptoms, abnormal gait, injection site bruising, injection site sterile abscess.
Immune System Disorders: Allergic edema of the face, allergic edema of the mouth, anaphylaxis, allergic edema of the throat.
Infections and Infestations: Pharyngitis, rhinitis, laryngitis, cellulitis.
Musculoskeletal and Connective Tissue Disorders: Muscle weakness, back pain, arthritis.
Nervous System Disorders: Dizziness, paresthesia, hypoesthesia, hypokinesia, tremor, somnolence, syncope, Guillain-Barré syndrome, convulsions/seizures, facial or cranial nerve paralysis, encephalopathy, limb paralysis.
Psychiatric Disorders: Insomnia.
Respiratory, Thoracic, and Mediastinal Disorders: Dyspnea, dysphonia,
bronchospasm, throat tightness.
Skin and Subcutaneous Tissue Disorders: Urticaria, localized or generalized rash, pruritus, periorbital edema, sweating.
Vascular Disorders: Flushing, pallor
***
In the US, The National Vaccine Injury Compensation Program was set up to compensate for vaccine related injury or death claims. Funded by 75c excise tax on every purchased dose of covered vaccine.
I suppose the needle could have hit a nerve, and since you have actually lost use of wrist and fingers, you do need to go to a regular doc and let him evaluate the situation, and he can then refer you to perhaps a neuro who can figure out the best way to fix what has happened to you. On the other hand, could be swelling has temporarily compressed some nerves, and whenever the sore place where the shot was calms down, so too would your hand function return. As for flu shots only being sore a few days, it can be sore even longer, those things are kind of hard on the tissues, each person is diff. But do go see your regular doc about this now, it needs to be in the records and a physician needs to make sure you didn't get some damage on your nerves going into your hand.