Thank you for your post.
Just go to the machine where you initially purchased FileMaker Go and launch iTunes. It should let you know there is an update available for FileMaker Go. If not, download from iTunes again, as it will check to make sure you are the purchaser and update your FileMaker Go application.
You could also go to the App Store on your iPhone and check the Updates section. That should list all apps with updates available.
All is well: I just waited until FM Pro and Go decided to update and they did by themselves. In addition, for others who have asked about FMGo and Mobile Me, I am finding my Go files in the iPhone, all nicely recent without my having had to do anything. This seemed to have happened during a Wi Fi update!
Thank you for your attention to my requests.