What features are you looking for? As others have said, if you just want somewhere you can store images yourself, you don't even need software aside from a webserver and something to upload with.
But there's also things like user accounts, tagging, browsing/discovery, plus whatever else gfycay does/did.
Anyway, just to actually give you a suggestion, chevereto is used by a friend and it's a lovely user experience (can't tell you about the admin side, though). [edit: This uses folders to organise - no tagging - so it might not meet your needs, which is why I was asking]
Have seen that one and looks like a nice option, but the site and docs have some gaps: can I put metadata/tags on the images in addition to the name for searches later? Also, can I put a description on the folder itself in addition to the description of each image? If both are "yes" I need to set up a small server.
You can add a title and description to images, folders, albums (what we've been calling folders), sub-albums, etc. You can search on those, but it's not a structured thing like tags. I guess you could just store some JSON in there but you might need to get smart with your queries to search. Afraid I have no idea if there's plugins, or even if what I've been using is a recent and/or unmodified codebase.
I think it's more designed for photo uploads, as there's an option to keep exif data, and it automatically makes images of different sizes (including your original, maybe massive upload).
All noted, thanks! I see there's a Docker option, should do a quick local install and see if i like it for my stuff, although my use case is less "vacation photos" than "sharing memes" like OP, hopefully it'll work for this