I would definitely go to see your primary care doctor
about this issue, since it seems to be quite severe and is persisting for more than one week.
Although I can't definitely rule this out without knowing more about your medical history, gout
would be extremely unlikely in someone your age, especially if you don't have any significant medical history. However, the bumps on your hand will need to be investigated closely by your doctor.
More likely, based on the nature of the pain you are having (burning and aching); you may have a nerve problem. You are quite right to raise the possibility of Guyon's canal syndrome, which involves pressure on the ulnar nerve and will cause nerve pain that in most prominent on the pinky side of the hand, just like you are having. Carpal tunnel syndrome
is also a possibility, although this tends more to cause pain on the thumb side of the hand. The fact that you use a computer mouse all day is highly suspicious, because this is often a setup for compression of the nerves in the hand or wrist, leading to the type of pain you are having.
Make an appointment with your doctor today!