I caught a shiny Rattata and a shiny Growlithe within 24 hours of each other.
The Growlithe was fucking gut wrenching because I didn't have any Pokemon weak enough to hit the Growlithe without killing it, and I only had 4 Pokeballs left. In the end I used my Tyranitar to weaken it down (Sandstorm) before catching it.
I bought a shitload of Pokeballs after that. I doubt I'll find another random shiny for a long time (I've found more in the past week than I have in the five years prior), but I said the same thing after the Rattata, so I'm not taking any chances.