The screen seems like it is stuck inside the kitchen faucet, when I unscrewed the cap on the facet, the screen doesn't come out. It's like it's UP in the faucet. The water pressure in the kitchen sink is like nothing! I'm just afraid to pry the screen out and then I will have water shooting everywhere and can't replace the screen.

With the handles in the off position you can pry the screen out and replace it. Better you should have a shutoff valve under the sink for the hot and cold. Turn them off.

When you get the screen out turn the water back on and try it, just to flush anything else out, and let you know where you're at, and if you need to do something more.

I must add though with the cap off, and the water on, you may get the screen out by just turning the water on from the knobs, or handles.

Let us know what happens please.