Q: iPhone storage full -- traveling...

It could be saying storage is full because the iCloud Storage limit has been met. To fix this problem you could turn some backup options off for iCloud, here's a link on how to do that:

Manage your iCloud storage - Apple Support

If that doesn't work the go to Settings-General-Usage-Manage Storage, and see what things are using the most storage. Deleting some of the extra items you don't really need could help.