Just some thoughts:
1) Clear the cache
2) Sign out and in again
3) Delete the app and reinstall. (You might lose your unsynced photos, although I doubt it.)
4) Start a new collection and see if that works better.
5) Check the settings in Lightroom Desktop Preferences, the Mobile tab. If you don't have many photos yet you could try "Delete all data" and start over.
The workflow does work, and it's very convenient, because you just shoot with the Lightroom camera and later the DNG files are in your desktop Lightroom. I've shot several hundred DNG images that way, since Lightroom has been able to shoot raw, and it's worked like a charm for me.
But sync is fidgety, with most vendors. For me, Lightroom claims that one image is syncing, and has been claiming that for several months now. I have no idea what it is, because I have the same item count on every platform, and the error box is empty. I just ignore it. For you, I'd give up on the two unsynced items and see if you can't get it working for new items in a new collection.
Barring that, I use ProCam 4 and it's a pretty nice app too, although it stores its files in the Camera Roll, and the raw files chew up an awful lot of space there. Lightroom Mobile doesn't do that; after syncing, just run "Clear cache" and the memory is freed. (The one thing I use ProCam--different from ProCamera--for is to take bracketed shots. It can take four raw shots, which can be processed into an HDR in Lightroom.)