I guess this is like a dunk and I shouldn't even respond, but I'd probably (from less) do /nick.*http and then hit n or N a bunch to jump around. Yeah, it's technically a regex, I guess, but I think it's probably the easiest/most common form. You don't really need to remember much of anything or understand how it works. You could be used to wildcards from a shell and just think "I gotta put a . in front of it sometimes for it to work".
I would not get more advanced than that, personally. Sure you'll have matches that aren't exactly what you're looking for, like that'd match both lines I said and lines mentioning me, and URLs that aren't images (better than trying to account for all types of image URLs, IMO) but I'll probably find what I'm looking for fast enough for it to not be worth looking up more complicated regex. Often I'll remember who posted something, too, so then maybe I'll throw their nick in the search as well, before mine. Or at least I could narrow down who posted it to a few people and just try a few searches pretty quickly back to back.
I would also say this particular search you're talking about would be fairly uncommon. I might even remember something like "oh, Bernie said that image was the funniest thing he'd seen all day, I'll search the word 'funniest' starting from the end of the file since it was under a month ago and should end up near the URL".