Help with removing scratches on 2010 black Prius

Hello all! So yesterday, I got into an accident, which unfortunately was my fault due to ice and slippery road conditions. I was trying to make a right turn and I tried to do a complete stop but my car would not stop even though I stepped on the brake pedals (again, due to the slippery roads filled with ice and sleet,etc). So due to this, I hit an oncoming car. Luckily, no one was hurt and the other vehicle sustained minor damage, and obviously, my insurance will cover her damages. But as for my car, I'm trying my best to save as much money as possible, I can obviously have the minor scratches and blemishes be fixed at a body shop but my deductible is a few hundred dollars but if I can fix it myself for a lot less, I'd much rather go that route.

So based on the insert picture below (I know the picture doesn't show the damage as clearly as I want it to be) but the scratches are underneath the Toyota emblem where the front license plate should be. Also, as you can see, my license plate is missing because it was knocked off during the accident. I think my front license plate took the brute of the damage since it fell off during the accident but my car still sustained some minor scratches near the drivers side of the front bumper. I will probably go to the dealership to have them install the license plate back on but does anybody know what products to use to remove these scratches myself? Meguiars? Wax or compound? Spot putty? Should I use sandpaper? Or should I just cough up the money and have the professionals do it? And since it's winter here, I understand it's harder to work on the car outside but like I said, I'm really trying to save as much money as I can. My car doesn't seem to have sustained any heavy damage. I don't see any dents or deep scratches so I'm hoping I can fix the imperfections myself.

Please any recommendations or any advice would be greatly appreciated. Thanks.

 

So I decided to wash and wax off the car to remove all the dirt, mud, snow, gunk, etc from my Prius to see what the damage really looked like (see attached photos below). IMO, it doesn't look as bad as I thought, but there is still a section of scratches near the license plate. I'm still debating on whether or not to go to the body shop to have it fixed but I'm still hesitant for 2 reasons. First, the deductible to have it fixed costs a few hundred I believe and I prefer to save as much money as I can, and if I do have it fixed via my insurance, I'm not sure if they'll raise my insurance fees even more for having it fixed. They'll probably raise it regardless since this accident was my fault but I'll call them to see if they have any accidentt forgiveness or any leniency due to bad weather and poor road conditions. Second reason I'm hesitant is that winter is still going to be around in my area for at least another 2 months(at the minimum, it could be longer) and if I have the scratches fixed, I'm sure my bumper will be scratched in no time due to the poor weather conditions in my area, with all the snow and mud and dirt and rocks and what have you bumping up against my fixed bumper. I mean, I could buy a car bra but I prefer not to.

As of right now, I'm considering buying some products myself to see what I can remove myself. There are no dents and there are no indents when feeling the scratches with finger. Based on what I've read, Meguiars seems to be the better of the rest for removing scratches. Based on the pictures, what do you guys think? What products would you guys recommend? Is sandpaper good for removing scratches? Or do you guys think I should just repair the scratches at the body shop?

Also, as you can see in the picture, one of the holes where the license plate goes was damaged a bit more severely than the other hole. I believe the bumper is plastic and not metal (correct me if I'm wrong) so the damaged hole shouldn't rust, right? Also, does anyone know who would be willing to install my license plate back on, preferably for free? Dealership maybe?

Any further recommendations or insights would be greatly appreciated. Thanks guys.