The heart rate thing and getting faster

So I am signed up for an 8.6 km race in 2 weeks. I know I can do 10 although this one is 4 laps with a nasty hill. This time I am only in for finishing, but the practice run they put on this sunday morning showed me how slow I really am. I had to push myself hard to keep up with the second slowest group out of 6 (Moms&kids in the slowest).

Rationale: To get faster I need to do runs where I exceed my comfortable heart rate....?

I added a 2 hour bike ride in the afternoon where I pushed a little too.
Whenever I "overdo it", and yesterday was one of those days, I get my PVCs (extrasystoles) at night.

Is that ok? I guess I build my basic cardio endurance with biking, so can I push myself as hard as I can on the comparatively short runs? At least sometimes?