It's simple economics. If farmers ger more for planting corn and soy, they will devote more acres to those crops and less to cotton. So the supply of cotton diminishes and price go up because demand didn't change.
The price will drop only if one of two things happen
1. Demand for cotton drops. I can't see that happening but it would eventually if the price kept rising.
2. Supply will go back up because farmers will now see a higher return for cotton and start planting more of it.
I am afraid that since the demand for corn as an energy source will continue to grow, every other product that is grown will become more expensive in order to compete for land. I can't imagine any other outcomes. It's market forces at work.
Boy, who knew I was actually paying attention in economics classes in college?