I would suggest putting a trap in the garage, with the door tied open, and a blanket draped over it. This will give the cat a place to feel safe when you go in there. When you are ready to take it to the vet (soon, I hope) you can untie the door latch and catch the cat with less trauma to either the cat or yourself.

There are rescues that will loan you a trap; you just have to find one that has one available. To buy one is about $65.

Once you have seen the vet, give the cat a box just big enough to lay down in and lay the box on it's side. This way the cat can feel safe, but you can still see it. Then sit on the other side of the room with smelly food and talk to it. Stay as long as you can, and leave the food where you were sitting when you leave. It will take several days for the cat to come to you while you are sitting there. When it does, let it feed without touching for a couple of days. If it lets you pet it, do so only for a minute at a time to start.

Poor cat is scared! I'm glad you could give it shelter and food. Thank you so much!

Be sure to put a litter box out too.