WillWorkForParts is absolutely correct that your bike is a girl's Schwinn Racer and everything else about it, except that it is actually an earlier model than a '66.
It's a late '50, early '60's model, as the pointed front fender was produced up until '63, and girl's Racers were discontinued after '62. Also the welded in kickstand didn't apply to some bikes at that time and that included lightweights (the Racer was considered a "lightweight" by the company; by '66, almost every Schwinn bike came from the factory with a welded kickstand). They got bolted on kickstands.
And yes, I'd start with the chain before tearing anything else apart. It's dry and crusty, it's one of the cheaper parts to fix, and it might solve most (if not all) of your noise problem. Heck, it'll be easier to pedal.