This might not be tennis elbow or golfer's elbow which is tendonitis at the elbow joint, for which you have been injected and treated. Since your pain is from tip of fingers up to your shoulder; this can be pinched nerves in the neck. This can be due to;
1) Herniated/degenerated disc in neck
2) Cervical spondylosis; bone spurs in the neck vertebrae pressing on the nerves.
Following investigations would be required;
1) X-ray of the neck spine
2) MRI of the neck
3) Nerve conduction velocity (NCV) study
4) Electromyography (EMG)
Following measures would be helpful;
1) Neck care in the activities of daily living.
a) No working on computer for more than half an hour in a single stretch. Same for TV.
b) Monitors and televisions exactly in front (180 degrees).
c) Contour pillow: Should fill the hollow when lying on back or straight. Available over the counter.
2) Cervical Collar or Brace
3) Cervical traction
4) Anti-inflammatory analgesics like Ibuprofen
5) Some physicians do give oral steroids in severe radiculopathy cases, in which pain is quite significant.
6) Physical therapy: gradually increasing exercises from passive stretching to active stretching and against resistance regime.
7) Electrotherapy in the form of TENS, interferential and laser and ultrasound.
8) Hot fomentation
9) Local analgesic patch / ointment / spray
You can consult following specialists;
c) MD in Physical medicine and rehabilitation
Please feel free for your follow up questions.