Welcome Brian, and yes with regard to shaving soap being better than shaving cream in a can, I'd say that's almost universally agreed upon here, as it's generally referred to as "canned goo". A good shaving soap or cream will be superior and may well help you solve the problem. As far a "scientific" my understanding is that ingrown hairs are caused by hairs being cut "too close" and growing under the skin. Shaving against the grain cuts the hair closer than with the grain, and also causes more irritation. By the way, I second @RyX's recommendation. The members of the 30 day thread are a great resource to help you work through the problem.
@KIBrian welcome from Central NJ. There are plenty of Jersey boys here. The Den is the place to solve your problem. You'll get plenty of great advice. Jump on in.