If it is ich, yes, you treat the tank. You probably know the life cycle and why this is critical. If not, here's a link to info on this issue from the Disease section: http://redirectingat.com/?id=401X512...icles-11660%2F
If the betta is the only fish in the tank, you could isolate it to a "hospital" tank if the main tank is large; the only advantage to this is less medication. The "empty" main tank would, after two weeks, be free of ich. But if it is not a large tank, I would just treat the betta in it to avoid further stress moving it. Stress takes a real toll on fish.
I said "if" because sometimes it can be something else, and sometimes these things clear up on their own. However, given the stress to the fish due to the cycling issue, it may very well be ich. Fish that are stressed frequently come down with ich (one reason why new fish so frequently carry it).
I have cured ich several times (I see it more than one with my experience should
) with Aquari-Sol. I like this product because it is less stressful on sensitive fish (such as corys if they were still alive, and characins), you don't need to fiddle with higher temperatures (though with a betta that is not an issue) and it works. The salt method also works but some fish cannot tolerate salt (corys and characins are not good candidates for salt treatments), I am not knowledgeable enough on betta to comment on salt; I know I would never use it on my anabantids, Chocolate Gourami and pygmy gourami, they are too sensitive.