Can I use a paint & primer combo on new wood?
The paint/primer should be fine, especially with two coats, but I typically begin with primer, as it seems (in my experience) that primer holds paint better and lasts a bit longer before requiring touch ups or repainting, and it's often cheaper to do a coat of good primer (match latex to latex, or make sure you follow the label if you use a different combo), then two or three even coats of less-expensive paint (paint+primer is almost always 2-3x more expensive than paint alone.

I wouldn't sand and re-paint, of course. You should be fine with what you have so far.

[Edit: one other note on paint+primer paints; make sure you read reviews or ask others about their experiences with the particular brand you're buying. A friend ended up with a patchy-looking paint job when he used one of the cheaper brands. I don't know if it was an isolated incident or if the brand is normally bad (or if he didn't mix the paint well!), but research before you buy.]