Can I recover photos that were being stored in a corrupt SD sector and then deleted after a phone restart? I have no idea how this is even possible, but let's start from the beginning.

I have a Samsung Galaxy S3. I went on a road trip this Memorial Day weekend and took a bunch of photos. The whole weekend I was able to view all of these photos just fine. However, while I was driving back my phone ran out of battery power and restarted (the Google Maps application drained it faster than my car could recharge it).

I did not notice until just now that all of the photos I've taken in the past 10 days are gone. What doesn't make sense is that I also have Google Photos installed on my phone and set to back up over WiFi only, however I connected to two (TWO!!!) wireless networks after I was finished with taking pictures. On neither of them did Google Photos trigger and upload the backups. Of course, now I've set Google Photos to back up over WiFi or a wireless network, so that backups are hopefully immediate.

Before leaving on this trip, I was attempting to add an album to my phone. While copying, I received a message somewhere along the lines of, "The SD card has been unmounted.", but upon a second try, I was able to continue copying to the SD card. I tried to delete four of the MP3s that were copied from this album later, and it would not allow me to. Also, after deleting the folder of these MP3s, it was replaced by the same folder with a single file ~TfsP or something like that.

I didn't have time to copy my files off the SD card and then do a reformat before my trip, so I just went with it like this. I was still able to play my music and, as I said, it supposedly was taking photos that I was looking at a day later.

If anyone knows how a restart of my phone deleted 10 days of photos, I would love to hear it, and if possible a way to recover them.

EDITS: Putting the micro SD card in an adapter and then plugging it into my Epson printer gives the message, "Cannot recognize the memory card or disc." Windows also gives me the option of "Scan and Fix" for drive H: (the SD card), but later says that it cannot access the drive. It is a Sandisk Ultra 64 GB, if that matters.
When confronted with such situations on a tight budget I have used the HDD software offered in the Hirens Boot CD.

www.hirensbootcd.org/hbcd-v152/

There are a few hard drive recovery options to choose from and I'm sure one of them will work providing the drive is not completely fried.
I have had many success stories in the past few years with the various tools offered by this useful collection.

Be sure not to try to write anything to your drive until it is recovered.
You may even be able to access the folders successfully using one of the alternative file explorers offered. There have been times when windows simply cannot read what Total Commander could.