For the last few months, when I turn on my faucet in my kitchen, the water seems to pump out of it instead of smoothly. If I pull the sprayer out and let it hang, it'll even itself out sometimes, but then goes right back to the other way. I have no idea why? Please help, it's driving me nuts.

Does your house have a pressure reducing valve?

Don't know what that is

A PRV valve looks like this, (see image) and is located where the water enters your home.
I have a different take on this.
Your diverter might have picked up some trash the prevents it from closing so it flaps sending a pulse through the water.
The diverter will be found under the spout in front of the valve.(see image) Remove the handle and the spout retaining nut. Pull the spout up. Check the diverter for trash or debris and clear the opening. Reassemble and test. Better now? Good luck, Tom