When is the orbit of an asteroid determined?
A few things to note on asteroids in KSP / ARM:
The orbit is determined when the asteroid is created. But any given asteroid may not persist, or de-spawn, even in a couple days, if you don't track it.
The act of tracking it is what makes the asteroid persist for any dependable time. As soon as you stop tracking it, it may de-spawn at any time.
Un-tracked asteroids have no real effect on the game. You won't notice them impact Kerbin, or crash into one of your space stations, or anything.
Tracked asteroids have very little impact on the game. When they crash into Kerbin... nothing really happens. In fact, they are likely to be removed when the hit the atmosphere, just like any vessel or rocket debris that is not being flown or within a certain distance of something being flown.
Q: So, my question is, have I basically screwed myself by starting to track this asteroid, or would it have always ended up on a collision course, I just would have not known about it?
A: It would always have been on a collusion course, and you just wouldn't have known - although it probably would have de-spawned before ever reaching Kerbin. You aren't screwed, and have a couple options:
Keep tracking it, and watch it crash into Kerbin (for as long as it exists). It won't ruin your game, or wipe out the Kerbal race or anything.
Stop tracking it - it will most likely de-spawn before reaching Kerbin. And even if it doesn't the chances of you ever interacting with any random asteroid is infinitesimal.
Either way, you can go about your Career Mode and deal with these asteroids only when you are ready to mess with them. (Or ignore them completely, if you want).
Asteroids normally either despawn in the atmosphere, or just hit the ground and bounce off. They do no damage whatsoever to the planet or any other object. Well, for now, at least.