Yes, a narrow-fit cycling shoe is exactly what you need. Narrow shoes are built on a low-volume last (the foot mold that shapes the shoe), giving you a slimmer forefoot and lower instep that hugs slim feet securely. The biggest benefit is eliminating that heel slip, which wastes power and can cause blisters on longer rides.
Narrow profiles are especially common from Italian brands like Sidi and Fizik, so those are great starting points. If standard shoes feel loose around your midfoot or your heel lifts when you pull up on the pedals, a narrow shoe will give you a much more connected, efficient feel.
Just be sure you truly need the narrow fit—shoes that pinch across the ball of the foot will cause numbness and hot spots within miles. When in doubt, it's better to go wider rather than sizing up in length to compensate.