Re: I'm going to need a bigger rod.......
Not sure about a flathead breaking the surface, but it's obvious that you're seeing fish like carp and others that will at least put you firmly in 6 or 7 weight territory. Should you hook one of these with your 3 weight, I'd save your fly line (and likely your rod) by grabbing the fly line with your hands and breaking off the fish without putting pressure on your rod.
If you're fishing these areas regularly, an inexpensive 6 or 7 weight isn't a bad idea to pull out just before sunset. Sounds like it could be a lot of fun if this is a frequent occurrence where you fish!