Country boy is the only one who is correct. Wax will do nothing. You need a da polisher and compounds along with someone who knows how to use them. Find a local detailer and see what they would charge for the spot. Should not be much unless it's the entire car. The other thing is if you went past the clear coat... that's a whole other story. If you're near columbus ohio I'll take a look for you.

One side is sponge and the other side is a scouring pad. You used the wrong surface. Go to a local autobody shop and ask them(as they have to see it) These are private enterprises. One body shop may say they have to clear coat the whole car....and the next shop may say only clear coat the hood...and the next shop says use Armour-All on it to reduce the visibility of the scratches.(because he can't even be bothered by you)

Every shop will give you their 2 bits worth and it all will be different. Remember that info and combine it and do it yourself.

Or put a decal on the spot.

Well if you go for a cheaper price then cheaper brand like turtle wax is your choice. I don't recommend sanding then putting all the paint back together, but hiding the paint like other brand of polisher may only help for so long since it only covering the scratches and using some wax for protection.

Plain car wax does NOT remove scratches! You'll need to use polishing compound on a small area to see if the scratches disappear. If not you'll need a more aggressive rubbing compound on the whole car BEFORE waxing with Mothers Pure Carnuba Car Wax.

Use an automotive paint wax to remove the scratches. It probably won't help much though, as you pretty much just washed your car with a sponge made of sandpaper...

Wash your car with a new micro fiber cloth and clean tap water. use two buckets, one for soap and one for rinse. Dry the car, buff the area with rubbing compound. allow to haze over. Clean the area, polish/wax the entire car.

Get some polishing compound and work the thing over with that and then wax it real good.

If you wish to know as to car detailing, why are you not asking a local business? This is not a directory to provide estimates that are worthless. I do not know why people ask for such things.

No problem you can wash off the grease, send it for detailing or just wax/polish it. It will look shiny and brand new

Here is a video to teach you the Top 10 Car Cleaning Mistakes so you can avoid this next time.