Again, "backed up" and "synced" don't tell me what you did. They tell me what you thought happened, and I know that those words mean different things to different people. You just repeated your original post. You did answer a couple of my questions, but the other things are still murky.
My inference is that your trip pictures are at iCloud.com; different pictures are on your iPhone and, right now, your iPhone Photos is not connected to iCloud.com. Is that right?
Not being sure what you did, I will say this: you're statement, " … I know that if I press sync now, it will erase what’s in my iCloud, as those photos aren’t on my iPhone," is almost certainly not correct. If you connect an iPhone's Photos Library to iCloud, then Photos will transfer all the pictures from the iPhone to iCloud.com, and then it will transfer all the pictures from iCloud to the iPhone, doing its best to avoid duplicates. This will be just what you want if my statement in the second paragraph is correct.