take a picture of it so we can see what you're dealing with.
if it is in fact a 16" schwinn, you must be REALLY small.
16" bikes were made for kids (5-8 years old).
if you have a 20" frame, and it is the stingray style, yes, a motor will fit.
how do i know? I built one. Mine is not an actual schwinn stingray, it's a knock off but it has a very similar frame design as a stingray.
the tricky part will be finding an engine that has the carb bolted right to the cylinder rather than one(that is the most typical) that has an intake manifold tube.
I got my engine off e-bay, and it's a typical china 50 c.c. 2 stroke, but there is no intake manifold tube and it uses a much different carb than the standard nt carb.
yes, it's only 50 c.c.'s, but it's just as fast as my 66 c.c. that's on my occ chopper.