Instead of re-importing the same images, you should do a search for those images in the catalog.
In Library, select all Photographs under Catalog panel and try to search for one of the images by its filename.
If you are doing extensive editing in Lightroom, you should take the backup of your catalog regularly so that you do not loose your edits.
While I don't know why your photos disappeared when you edited the photo in Photoshop (they shouldn't do that), let me advise you to not try to import a photo a 2nd time (this never helps, it usually makes the problem worse),; and don't try to synchronize folders to fix the problem either (this never helps, it usually makes the problem worse).
Instead, when Lightroom is telling you that the photo is a duplicate ... then what you need to do is find the photo in Lightroom. That is the only way to fix the problem. You can click on All Photographs in the Library Module (its on the left under Catalog), and the search for your photo by file name. Again, let me state that this is the only way to fix the problem and not make it worse. Once you have found the photo, you can then find the folder it is in according to Lightroom by right-clicking on the photo and then selecting Go to Folder in Library.