Power steering problem

I have a 2001 mercury sable (though doesn't matter) that has a power steering problem. I think I need a new pump, but want to make sure it isn't some easy fix. I hit a deer and punctured a small hole in the cooler line. I drove it home about 3 miles and while there was still fluid leaking out, I'm sure it was close to empty. (I know bad) I replaced the cooler and bled the air by jacking up the car and turning the steering wheel from stop to stop about 20 times and there was no more bubbles surfacing. Problem is when I start the car the fluid drops way down and the pump whines and when I shut the car off it overflows to the point fluid sprays out of the vent in the cap and the fluid is where it's supposed to be (minus the overflow spray). There is no leaking from any of the lines but the fluid is foamy after the car shuts down. Seems like there is air in the system, but damned if I can get it out. Am I over looking something or did I fry the pump? Any info would be greatly appreciated, thanks.

Normally foamy fluid means air is still getting in the system. You sure you don't have another leak?

Normally foamy fluid means air is still getting in the system. You sure you don't have another leak?

I checked everything and couldn't find any leaks, I think the foaming is coming from the low fluid when it's running. It's so low it introduces air into the fluid, but then over flows when I shut the car off.