Auto Insurance Claims: Other driver at fault, totalled vehicle, scan x, settlement value

Question
I have (had) a 97 Camry with 110,000 miles on it that was totalled the 2 days ago by another driver who hit me head on. Both my Ins Co. and her Ins. Co. valued the car @ around $5400, but that won't do much to help replace the vehicle I just lost, which was in exellent condition before the wreck. Also, I've been having headaches and could have a concussion. On top of that, I work as an accountant and at this time of year have NO time to look for a new vehicle until April 15th. Can I get the Ins. Co. to pay for a rental for the one month since I am unable to look for a vehicle due to the nature of my job? Also, can I use these factors to get more from my insurance settlement?

Answer
Hi Ryan,
I'm sorry to learn of your accident.  In reality, you have two separate claims.  One for the damage to your car and one for your personal injury.
In my opinion, the most important one is your injury.  You need to go to ER for a complete check up including CT scan, X-rays and possibly an MRI, then see your personal physician for referrals to specialists who will treat your injuries.
Yes, I realize that this is the busiest time of the year for your profession but if you have any serious injuries, their settlement value is far more than you could possibly earn in the next three weeks plus your lost wages will be reimbursed as part of an injury claim which also includes reimbursement of medical bills and a fair compensation for your pain and suffering.

If you feel that the $5,400 settlement for your car is not enough, you can do all the work by researching it's value and present it to the insurance company and argue for a higher settlement.
Once you reach an agreement with the insurance company for the value of the car and they write you a check, the rental usually stops at noon the following day, although some companies will let the rental run for two to three days so you can shop for a car.
There is no way that any insurance company will continue to pay rental until it's convenient for you to shop for a car.

I hope this information is helpful.
Your feedback by rating my answer will be appreciated.
Sincerely,
Bennie
San Francisco Bay Area