Ok. I decided to use my pokeradar to find a shiny for the first time, and after chaining ten shellos, I found a shiny... buizel. Is that supposed to happen sometimes, because ive heard of similar things happening to other people too.
No, that's not supposed to happen. However, it is possible considering that your chain may have broke by encountering a different Pokemon and you encountered a shiny not part of the chain you were just in.
Just take it.
Source: Experience and there's nothing about it here.
Your chain broke, and you randomly ran into a shiny Buitzel (with the usual 1/8196 chance of it happening). that is the only reasonable explanation other than your game glitching out.