I'm not an expert but I do read a lot about this stuff. I would say that you're going to be able to build 1-2lb of muscle in a month, MAX. And that's with serious weight training with heavy weights and a high protein, maintenance+ diet. You might be able to add a couple of pounds of muscle when you first begin weight training while eating at a deficit, but that won't last very long.
New muscle is probably not the source of your scale fluctuations. It is very common for muscles to hold onto water after exercise though, especially when you first start. That, to me, seems the much more probable explanation.
"Losing weight is easy; I've done it dozens of times."
(with apologies to Mark Twain).
Ultimate goal: Size 10 clothing.