Hi AggieYen
Sorry to hear about your Betta's fin rot problem. Yes, it happens for sure.. but the good thing, as you already know is that it is treatable and easily remedied with medication, and water changes. IMO if you have the medication available I would start it soon. You mention that half of his tail fin is gone, that would indicate to me the need to start meds soon and not wait a week. Maybe I am being overly cautious on this, but why wait til it gets even worse?
As far as the water current goes, this is a reason that I have been researching the sponge filters for betta tanks. Maybe while your guy is healing you can use one of those to cut down on the current? They are not expensive at all, and hook up to your air pump.
good luck with Champion... hope he feels better soon!

~ kate
EDIT: oppps.. I read it to say that half his tail fin was gone, my fault. A portion of his tail fin is gone.. not sure how much is.. so I was really concerned, sorry for the mis read on my part.