Let the 7-up go mostly flat (stir it and let it sit for a while, or pour it warm into a tall glass then add ice, etc.). Then drink it, and eat a small amount of saltine crackers.
Letting the 7-up go flat makes it less irritating to your stomach, so it won't be as likely to set you off. And, if/when it does come back up, the flat 7-up doesn't add to the irritation of your esophagus.