The should be a file manager app on the phone (look in the app drawer). You can use that - it shouldn't be necessary to use a PC and I don't think the gallery app supports file moves.
It's also a good idea to set the file location to the card in the camera's settings - it'll be one of the options there. If you do that and then take a picture, that'll create the relevant folder and you can copy all the other photos there to keep them all in one place.
Always copy and then confirm that everything's OK before you delete the originals. There is a move option but, if anything goes wrong, you can find that although the copy stage fails, the delete one completes just fine (been there, done that :smileyembarrassed:) and you've lost the lot!
Edited to add: as a belt 'n' braces backup, it's a good idea to set your photos to sync with Dropbox or Google Photos. That way they're safe if anything goes wrong on the phone. It's a convenient way of transferring them to a PC, too.
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