Congrats on the Shiny Drowzee! I too didn't know about Shinies back in the day and would've failed my first encounter as well if the game had let me run away from that Golbat.
I was determined to find a Shiny before clearing VC Gold, so I did a lot of grinding and found a Shiny Tangela just for it to flee... though I wasn't terribly disappointed about that since Tangela was the Shiny I least-wanted in that route. I kept going and found a Shiny Weepinbell, which I was much more happy with than Tangela. Lickitung would've been nicer, but pitcher plants are cool!
After clearing the game, I went back to try SRing a Shiny Tyrogue but grew bored of the repetition and decided to focus on getting my team to lv100. I was training in Mt. Silver when a Shiny Misdreavus caught me by surprise! She's now my main 'mon in VC Gold.
I decided to change locations while grinding in hope of finding another Shiny and, while crossing my fingers for a Shiny Girafarig (or Venonat), I found a Shiny Mareep. That's also cool. PURPLE SHEEP-DRAGON TIME!
I headed back to my original hunting route hoping that I might finally score a Shiny Lickitung while grinding, but a Shiny Bellsprout popped up. Pretty disappointing since I already had a Shiny Victreebel, but I caught it anyway. (Too bad I didn't know the Repel Trick at this point!) It's on Ultra Sun now, but I haven't raised it.
In fear of finding a repeat Shiny, I changed locations yet again. I remembered that you could fish-up Lv40 Corsola (one of my favorite aesthetic Shinies) inside the Day-Care area, so I figured I'd try my luck there. I had forgotten that Krabby and Kingler also appeared and I really didn't want either of their Shinies, but I lucked-out and hooked a Shiny Corsola!
All of this happened within a month's time. I've never had such luck!
As far as Shiny difficulty goes, these games have the same full-odds Shiny rate as any other pre-3DS game: 1/8192 (full-odds Shinies are twice as likely to appear in the 3DS games). The hardest games to find Shinies in are, in my opinion, the Gamecube RPGs -- Colosseum and Gale of Darkness -- simply because catchable Pokémon don't appear as often.
