I'll 2nd what Iridflare stated about shooting in RAW. Phones, or at least just about all of them, don't shoot RAW but JPEG only. In addition, phones generally cannot read, and therefore display, RAW files either.
The file system used by your camera isn't the same as that used by or understood by your computer and vis versa. Your phone will not be able to properly read data from an SD card that was formatted using the file system that the camera installed during the format process. This is why your phone cannot "see" the files on the SD card that you used in your camera.
Try copying the files onto your computer and then copy from your computer to your phone. You can also email the photos to yourself, open that email with your phone and then download them that way.
Why you cannot see the files when inserting the SD card in your computer? This may be a problem with the card or the way it was formatted or maybe it has become corrupt when you inserted it into your phone. Maybe the phone did something to the file system on the SD card without you knowing?
In any event, try using a file recovering app such as Recova. Download and install the app onto your computer, not your phone, and see if that allows you to gain access to the files.