The reason Texas personal injury lawyers may salivate is that the case has potentially large damages as there is likely little question about her fault, only a small amount of potential reduction because of possible contributory negligence on your part, and a permanent injury - severe scarring.
The first thing they'd consider is whether there is a products liability case against the manufacturer of the chainsaw and the firm that sold it to you, perhaps for a manufacturing or design or labeling defect. That would generate big money, but is usually hard to prove. The manufacturers have major insurance coverage behind them and their insurance companies are not in the habit of paying claims quickly or admitting liability. But let's assume there is no product defect.
Absent such a defect probably the only one to look at is your mother (and perhaps father). The issue is what assets does she have and how much liability insurance did they carry on her homeowner's policy. And unless you are prepared to sue your mother -- and it does not have to be a vicious suit -- forget about it.
Now the fact that her homeowner's insurance company might know that in front of a jury it might get hit with a big judgment that it hwould eventually pay would, you think, motivate the insurer to pay you what the case is worth and you'd be able to avoid paying a lawyer a fee that might range from 30% to 40% of the recovery, plus expenses. So if she had a $250,000 liability limit on her homeowners, and you could read something that says for facial disfigurement a jury in County X awarded $200,000 to John Jones, my guess is you might think you could go up to the insruance company and say, "Hey guys, give me $150k and you'll save the cost of litigation and I'll agree to that, and if not I am getting a lawyer and you'll pay more." Sounds fair to you - you get $150k, the insurance company saves $50k (plus the costs of defending the suit - and they WILL defend), and you face no lawyer bills and no delay, right? WRONG.
That's not the way the world works, and sure as heck not the way the insurance companies work. They know that lots of people in your situation would never sue their mother or other family or friends, regardless. They also know that if there is no law suit, they'd have no money to pay out. (And they have actuarial data that tells them what percentage of cases are dropped if they "Just say no.")
Insurance companies also know no case is fool proof, and even what looks like an open and shut case sometimes gets surpise verdicts. (Do you REALLY think OJ should be out walking the streets?).
As for the other cases, they really know all the data, you don't. What cases settle for, what juries award, and when and where, etc. You don't. They'll distingusih your case from the others. And they'll know if a $200k verdict elsewhere was an anomoly or based on the lawyer and where the case was tried (and a $200k verdict in Houston is probably easier to come by than one in Midland), and how sympathetic the plaintiff was, etc.
They also key on who is your lawyer. If Joe Jamil personally handles it, the case is worth more than if Joe Schmo handles it, because they know Jamil only takes huge cases and has clout. Get yourself a Texas personal injury attorney now. If you try to handle it yourself, even if you were alawyer, they'd say you are a jerk and treat you accordingly. (One exception --if the liability amount of her policy was relatively small, and they saw a big judgment as likely, they might "throw in the policy limit" to avoid having to defend and possibly risk a bad faith claim down the road.)
Insurance companies are pretty sharp about spotting phonies and fools, and that's how you'd be branded. But if you go in to see them in the circumstances I suggested, you'd have a fight on your hands to get even 10% of what the case is worth, and before you are done you'd likely screw things up so that even if you hired the best lawyer in Texas you'd be likely to get less than half of what the case would have been worth if you didn't approach them -- and that's before legal fees.
If your mother has no homeowners, then unles you can find someone else who is at fault -- such as am employer, neighbor, etc. the only source of funds would be your mother's assets.
For some information on damages, look at this:
http://injury.freeadvice.com/injury_help.php/117_156_835.htm