I just acquired a 6mo old pittbull female and she was attacked by her mother a while back. All wounds are healed but she has been very lathargic, and can't go far without falling over. Its like she is very dizzy and can't focus. What can I do? The animal clinics in my area would just want to put her down and that is not an option. I usually do all the med care for my animals myself. Since the vets in my area just really don't care...

Why would the Vet put her down? What am I missing?

What can you do... you can take the dog to the vet for proper care... that's what you can do.

"very lathargic, and can't go far without falling over. Its like she is very dizzy and can't focus."

Why would anyone sentence a dog to living like this?

Take the dog to a Vet! Now!

Why would you just assume that the vet would want to put her down, is she in that bad shape?
I'm sorry, but to me that seems a little selfish on your part, to make her sit around sick is doing no one any good especially not her.
You can't treat something when you don't know what the problem is.
And to live like that is unfair. Without a vet visit you will not know what is wrong with her and whether she can be treated.
If you don't trust a particular vet then go elsewhere, but you need to get her seen.
BTW was she treated by a vet or yourself after Mom attacked her is it possible that it could be related? How long ago was that?
I mean, things that come to mind are unchecked infection, muscle damage from lacerations, nerve damage and more.

"... since the Vets in my area don't really care ..."

Last time I heard this a dog was suffering and the Vet recommended that the suffering be ended. Pet owner was enraged.

Sigh.

Sounds like vertigo which is fixable