Good luck to you and your daughter! I'm sorry to hear she's suffering with TOS at age 19, but glad to hear she found a doctor who figured out what was going on!
Did you have specific questions about recovery? For me, I was in the hospital overnight and most of the following day (discharged around 7 PM). My surgery lasted about 2 hours and immediately upon waking there were people ready to manage my pain. They gave me an injection and monitored pain, when it was obvious that drug was ineffective for me, they switched to another. While I was in pain when I first woke up, they got me set up with a pump ASAP, complete with a button I could push to regulate administration. They took it away from me the next morning around 7 AM to see how I could manage without it - they assured me I could have it back if I felt like I needed it - and started me on oral pain meds. While I would have liked to have the pump another day, it was manageable with the oral meds and since a) I wanted to get home as quick as possible, and b) I'm always paranoid about getting addicted to something (family history), I let them keep it. :-)
I had a small chest tube attached to a bulb to remove fluid; this was removed right before I was discharged (literally, about 3 minutes before I checked out). I had to do breathing exercises with a spirometer every hour for the first 24 hours (a plastic spirometer goes home with you and you continue to do this exercise on a more modified scale at home).
While in the hospital she'll be "doped up" enough to be a bit unsteady on her feet and hooked up to IVs, so she should expect to be helped to the bathroom (although she should not need help IN the bathroom); and no bathing or showering. The staff is great; just let them know what your needs are - while I was on hydromorphone, it made me itchy (extremely common), and they were great about getting me antihistamines and discussing whether I'd like to change drugs (I opted not to change, the effectivity of the drug was, to me, well worth the itchiness). Expect to be woken up about every hour, though - people checking on you, taking blood, ensuring pump and IVs are functioning properly, etc.
I was not put in a sling or bandaged at all. I was allowed to use the arm for things like eating (and bathing, once released) but advised to take it really easy with the arm. My instructions were to do no driving for two weeks plus however long it took to get off the oral narcotic pain med entirely, so I actually didn't drive for 3 weeks. When I did start driving, it was surprisingly uncomfortable for about the first 10 days - you don't really hold your arm that way doing anything else. The first week post-op I was taking the max dose of pain meds at the exact interval I was allowed (and not a minute earlier or later, even in the middle of the night!), but then started tapering off. For the last week, I was mostly taking them just at night. Still, it was a solid two weeks of not doing much other than watching TV while lying on couch or bed, and sleeping - it was bothersome to hold a book or phone for too long, even - the worst part was that I invariably sleep on my side, so when I would roll to my side during sleep, it would wake me up.
I had one small setback on day 4 when I woke up with severe pain in my chest. I went to the ER; it was most likely spasms of the intercostals, but they did a full CT to ensure I didn't have a clot or pneumonia. The ER doc put me on antibiotics "just in case." I got the feeling he was one of those doctors that feels every surgery should get post-op antibiotics. I don't know if that was necessary, but I didn't get pneumonia, so I won't complain. :-)
I started PT at 4 weeks post op and went back to work on light duty about 2 weeks later. I am still on light duty at work and not allowed to do anything "jarring" yet - i.e. jogging, horseback riding, etc. Dr. Pearl said it would probably be at least 12 weeks from the date of surgery before that type of activity could be considered (I'm supposed to get re-evaluated by him at the 12 week mark).
Is your daughter on medications now? If so, she will likely stay on them during the course of recovery (along with Rx'd pain meds) and not discontinue them until it can accurately be determined (when she does discontinue them) that any pain she feels is not lingering surgical pain vs TOS pain.
Naturally the course of recovery can vary - the complexity of the individual surgery is a huge factor, as is severity of condition, individual fitness, tolerance of drugs, adherence to the instructions and restrictions, etc. Thus far mine has fallen into the "average" category (thankfully!).
Let me know if you have specific questions!