If you're only looking for someone to pay medical expenses, you probably don't need an attorney right now. Many states (like my state, Kentucky) have mandatory coverage for medical expenses in automobile coverage. Check your policy and contact your insurance agent for more info.
If you do decide to hire an attorney, hire one the same you'd hire somebody to perform some other service for you, like paving your driveway, taking a tree out of your yard, etc.:
--Consider feedback from friends, both positive and negative;
--Don't hire the first one who says s/he'll take your case--s/he may not be very good, or very experienced in your kind of case, or s/he may charge much more than the going rate;
--Sit down and talk with them, and make it a situation where you're interviewing them as much as they're interviewing you--find out how much experience they have with this kind of case, whether they'll be handling your file or whether someone else in their firm will be taking primary responsibility, how they expect the case to proceed, etc.
--Judge how likely they are to handle the case assertively. The #1 complaint most folks make about attorneys is "I gave the guy/gal my case and I never heard from them again--they didn't keep me updated on my case status, no one ever returned my calls and I had no idea what was going on." You'll be giving them a good bit of the fee for the case (anywhere from 33 to 40% is what most Plaintiff's attorneys take as a fee, plus expenses). You have the right to expect prompt, quality representation. If you get the idea you won't get it from that attorney, keep looking.
Hope your daughter feels better. (And or course, don't consider this a substitute for legal advice. See an attorney in your area for that.)