I don't know about Nexium, but I can tell you what worked for me. Another mom told me to try chewable papaya tablets after every meal. No medicine, just 100% papaya, so you don't have to worry about chemicals or side-effects.
It won't completely stop your heartburn, but it really helped me a lot. The enzymes found in papaya, help to neutralize stomach acid. It helps to create a healthy gut before heartburn flares up. And the tablets are kind of yummy too.
You can find papaya tablets at any health food store, such as Whole Foods or Mustard Seed Market.