Darn, it looks like Photobucket just changed the policy recently. Reading a bunch of comments on Twitter about people suddenly losing the ability to embed their photos in 3rd part sites without an expensive subscription. Your photos should still be saved on their site though, just without the ability to share.
I use
https://postimage.io/ . Much cleaner and simpler than Photobucket without all the ads and clutter. See if you can download all your photos and then re-upload to Post Image. Annoying as heck to have to update all you links though
EDIT: From their own TOS. Wow, what a rip off....
EDIT 2: Wow, dodeca facepalm:
https://www.pcmag.com/news/354711/photobucket-breaks-image-links-across-the-internet
^Image hosted for free at Postimg!