Hi all, I'm a new to bike maintenance and forum use, so go easy on me if I've done anything stupid in regards to either of the two. I'd really appreciate any and all help.

I recently went out for a ride on a popular trail near me and near the end of the ride I was getting some chain skip on my second chainring and fifth or so rear sprocket. It's a rather new bike, the cassette and chainrings are plenty healthy, so I figured the chain/drivetrain had just become very dirty and sandy. I'm tight on money so I thought I would tackle this myself. At first I only had 91% isopropyl alcohol, so I let the chain take a bath in that while I went at it with a thick bristled brush, and a lot of the grime came off, but not all. I washed it out with water, blew some compressed air through it to get the water out, and let it dry in the sun for about an hour.
After this I realized my rear derailleur pulleys looked quite dirty so I went out and bought some concentrated all purpose Simple Green, diluted some in a spray bottle, and hit the rear derailleur, cassette, and chainrings with that, let it sit, scrubbed at it a bit, then washed it all off with a hose on low power. I also figured I might as well let the chain sit in some simple green, which I did, and it got the chain looking much cleaner than the alcohol had. After I dried it all off, everything looked nice and shiny, so I put the chain back on and went about putting a drip of Park Tool synthetic blend chain lube on each roller. But even after doing so, I noticed a really grainy, gritty noise occurring rather loudly in the chain, along with a loud click happening in the rear der/cassette area every few seconds.. my cassette and chainrings are totally clean and brushed, so this leads me to believe dirt or sand is actually down in the rollers of my chain and is affecting the entire drivetrain. Is there an easy way to go about cleaning this and making my bike rideable with the supplies at hand? Also, am I supposed to actually grease the cassette and chainrings themselves with bearing/bike grease?

Thanks much for reading my lengthy post. Any advice is appreciated greatly. I don't have the spare cash to go out and buy much of anything else right now, so any tips using what I have at hand (Simple Green, Park Tool chain lube, and PT "polylube" grease) is preferred, but if you know of another fix please let me know.