Stray cat that got away

My friend and I were out on a walk near my house. We were on the way to the store when we saw this black and white longhaired cat on the other side of the road. We took a different way back home and we saw the same cat; it was being barked at by a yappy little dog. Upon closer inspection, the cat's fur was all shaggy and a little matted. It had a cut on the top of its head that looked like it was healing. When I touched its neck I could feel it was covered with scars. Its eyes look okay for a stray. I used my friends sweater for a blanket of sorts and started carrying the cat home. About a block and a half from my house, we got closer to heavier traffic and the cat got spooked. I was wearing a long sleeved sweater and he scratched and bit my arm a little. Right after that he jumped out of my arms and ran away. Anyway my arm is a little scratched up, not that bad considering it scratched my jacket and not my skin directly...it didn't break skin and is not bleeding. I washed it up and put polysporin on it.

Anyways my question is, should I go back and try and find the cat? My mom would probably get mad for bringing a stray home but I want to take it to a vet at the least.

I'm wondering if it's worth looking for the poor kitty--I mean, I want to, he was just so beat up. But I don't know if I want to risk getting hurt even more, or having him get spooked and hurt anyone else in my family, human, cat, or dog. And what will I do with him? I could keep him in the basement, but after he gets well, what would I do? I have no idea how he is with other cats..

Here's two pictures of the little guy and my arm:

If you could both feel all over him, and after it carry him half the way, he cant be truly feral, and apparently isnt that difficult to handle. No more than many home cats.
He will be probably a good family cat with time and some fostering.
You can even try to set up notices on message boards around where you saw him. He perhaps do has a owner??
You can do it after you get him into your cellar, or instead.

It seems you dont need a human trap, as it seems you can handle him...
Use a common transport box for transportation. Best. Otherwise you can probably use the basket for wash-clothes. These here in Sweden are made of plastic, with some holes in the sides and a lid. I quess these are common also in Canada.
These are excellent as reserve- transport boxes.
Have something in the bottom to lie on. And tape the lid. Voilá!

You must of course agree with your parents it is OK to help the cat. It will also be a lot easier for you with their approvance and perhaps even their help.

Good luck with your quest!