Rear-ended at 45? That's brutal.
Like some others have said, your wife may feel ok today, but in the next day or 2 it's very likely (I would say a certainty) to degrade significantly with soreness and pain, as well as general lethargy and irritability (back and neck injuries like this have a real negative effect on mood.) Also keep an eye out for pain in her hands, when rear ended if she had her hands on the wheel it can cause damage from her body jerking and then smashing.
2 things: 1) Talking to a lawyer is in your best interest. 2) You should get her in to see her physician, and talk to them about seeing a pain specialist soon, one that deals in traumatic injury.
Also, don't put this on your medical insurance(they will end up denying charges and it makes a mess), you need to tell your dr. (and any other medical facilities that treat her for this) that it is a car accident and to open an account for it. Most facilities will tally up the bill until such time as you are ready to deal with the responsible insurance. I recommend talking to the lawyer about the best way to handle it since the relevant billing laws may be different in your state.
~edit~ Also when talking to the other driver's insurance, do not commit to anything now, let them know that your wife has gone to the hospital, and may be receiving further medical treatment, do not discuss any compensation for medical until you have spoken to a lawyer and have a good sense of the scope of potential medical costs.