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.