Sounds like a Rufous Hummingbird. They have that kind of metallic high-pitched wing sound. We have lots of them now at the farm. We also have the smaller Calliope Hummingbird, which although smaller has a deeper wing sound with no whistling.

Rufous hummers will do this climb-and-dive loop routine for a mating dance, with a little butt-wiggle at the bottom. You get this "WEEEeee--oooo-chee-chee-chee-chee" sound from that, then they'll do that side to side hover and you hear "cheem-cheem-cheem..."

OK, the first person to laugh at my sound effects renditions gets a whack...
I'm laughing, but only because you nailed it perfectly! That's exactly what it sounds like.

A lot of the hummingbirds I see are sort of plain colored, but there are a few that are an iridescent greenish yellow or iridescent purple on their chests. I've seen some with a bright red band around their necks too. I have no idea what type they are, but they sure are pretty when they stay still long enough to get a look at.

It's fun to watch them chase each other through the trees. They are like little tiny fighter jets in a 'dogfight', complete with daredevil moves. I often wonder if hummingbirds experience fun or enjoyment. You'd think they have to. What a thrill that would be, to fly like they do.