Car accident/new car help!

2 weeks ago my 6 week old daughter and I were involved in a car accident (not at fault) which totaled our new car that we had just purchased in May of this year. Thankfully no one involved was injured but of course we're now dealing with the stress of car shopping when we weren't planning on having to and dealing with the insurance companies. We were financing our car and had only made 2 payments since purchasing it before it was totaled. Our insurance has sent out the settlement payment to our lien holder, which they will receive next week, and we are now left with filing our GAP coverage claim. We need a new car asap as my husbands work car has no a/c, a falling headliner, and sounds like it needs some serious TLC. None of which I feel is safe for my newborn to be riding in. While waiting for our insurances to handle the claims and payout what is due is it possible to apply for another loan as if the car is already off our credit? Since it's totaled and we have proof that it will be off our credit once insurance is done would that affect the amount we'd receive or our APR? I'm really hoping someone else has experienced this and could give some insight. We need to be in a new car by next weekend and of course insurance is going to take longer. Thanks!