Gout is the most unlikely of all possible causes that might explain your symptoms! Gout is a relatively rare metabolic disorder wherein large quantities of uric acid are produced. Uric acid is discharged through the urine in large amounts and causes development of renal stones. Some quantities of uric acid crystals are disposed of in the tissues around the joints, especially on the foot. Chronic inflammation develops around those crystals which leads to very painful growth. It doesn't seem likely that you have this disorder. You probably have an infection on the skin of the fingers. Go to your doctor to check it out.