First brew, I dunno about the yeast.

This morning I boiled up a Belgian Harvest Ale, but I think I mishandled the yeast out of sheer ignorance.

I smacked my Wyeast a few days ago, but it didn't swell until last night, perhaps because of temperature? The real problem though, came when I went to pitch the yeast, and opening the package to find an extra packet. Confused, I decided to pitch the yeast and cut open the small inner packet and pitch that too. Later I found out that the small inner packet was the "nutrient packet", but I'm not sure if it it harmful to my beer or not.

Also, if I need to pitch new yeast, do I have to order the same strain from Wyeast? Or can I find something similar at my local homebrew shop?

When you "smack" it is supposed to rupture the ball, feed the yeast, and get them into reproductive phase. It is probably fine.

That said, you are generally underpitching with a smack pack without making a starter, and in your case you will be underpitching more severely. Stressing the yeast for a Belgian is not always a horrible thing though. I would give it 48 hours before worrying about repitching, and not repitch unless I could not measure any activity at 72 hours.