The only way to get rid of tophi (other than surgery when they get so big they burst through your skin) is to lower uric acid below 6mg/dL.
The remark about surgery is supposed to shock you into recognizing the severity of tophi. They are a strong indication that uric acid crystals are building up around your body. Quite often this is a slow process that does not always bring typical gout pain. They become serious if you do not lower uric acid - much more important, long-term, than managing pain.
Whether you can do this with diet and lifestyle changes, or medication, will depend on many factors. Mainly these are how high your uric acid level is, how long you've had gout, and whether your gout is caused by hereditary, kidney or lifestyle factors.
First step is to arrange regular uric acid tests. A consultation with a rheumatologist may help you understand the severity and possible causes of your gout, and help you decide how to treat it.
Good diet and regular gentle exercise can only help. You are doing right to drink plenty of water. Soda can be a problem, but mainly from the fructose it usually contains. Carbonated pure water is probably beneficial, but tap water is usually cheapest if you live in an area where quality is good.