If you are still looking for an alternative to Photobucket to host your adoptable images, these are some suggestions from other forums I visit:
http://imgur.com/
https://www.flickr.com/
Facebook (create a private album, upload your images, then right click on each one and choose Copy Image Link to post it here)
Note: I don't think Discord is a good place for saving your images because it seems like some of the images break over time. I've had a couple images I posted here in a brag thread that aren't working anymore that I linked from Discord.
Also, not entirely sure how reliable deviantart's sta.sh is, but it's done the trick for me so far in hosting images.
Good idea! Yeah I'm pretty sure the Stash is private and no one can see it unless you share the image link with someone.
Yup! You can also share folders in stash, not just individual images, which makes it slightly easier than FB.