Not sure if you are talking about the same thing that's happened to our driveway. Ours is cracked and parts have "settled" lower than others.
We had a drain put in our driveway, the prior owners had the gutter downspout just draining on to the driveway which ruined it, not to mention it didn't help that whoever poured the concrete initially did a good job. The guy who did the work only does concrete work. He can patch the cracks, or cut out the bad areas and pour new. I woudn't never think about trying to raise any parts of it, but your case may be totally different than mine.
If you want you can P/M me and I can give you his name. May be worth the call to see what he may suggest.
I did a quick look-up on Google to see what "mud jacking" was just now. Seems this company does what you're looking for - know nothing about their work, but would love to know what you find out if you call/use them
Mudjacking For Sinking& Settling Concrete Repair in Columbia, Augusta, Greenville, South Carolina and North Carolina
I've heard of RamJack, but not sure what they cover, I know they do foundations for homes, not sure about driveways.