Hmm.. I scanned the catalog photo of the 1989 Prelude and used a Gerber Variable Scale to derive dimensions using the wheel bead diameter (622mm) as a fixed dimension. All of the '88 and '89 Preludes, including the small frame sizes, were equipped with 700C wheels.

The catalog photo is of a 23" (58cm) frame, and the head tube angle for the 23" frame is listed in the specifications as 73°. I'm not sure whether the 19" (48.5cm) frame had a different head tube angle or not. I know the 1988 19" road Paramount frames had a 72° head tube angle, while the 1988 23" road Paramount frames had a 73° head tube angle, but am unsure of whether or not Schwinn had the more relaxed geometry on the Prelude smaller frames.

It looks like the 1989 Prelude frame I scanned has ~45mm fork rake which, with 700C wheels and a 73° head tube angle, gives it ~50mm of trail, which should provide great handling.

If the OP could provide a profile picture of his bike taken at some distance and using a telephoto lens to minimize distortion, we might be able to see something amiss. Based on conversations with many late eighties Prelude riders, I can say with certainty there's something wrong with the OP's bike; it should handle like a dream.