How Should I Handle Insurance Claims For Two Accidents In The Same Month?

November was a rough month for my partner and me. She drives a 2018 Jeep Compass with a market value of approximately $10,000, but she still owes $19,000 on it. Unfortunately, we were involved in two car accidents within a three-week span.

The first accident occurred on October 28th, involving a three-car collision caused by a hit-and-run driver in a stolen vehicle with no license plate. I was the third car struck. From what we've gathered, it seems we would need to file a claim through our own insurance, which means paying a $500 deductible and potentially facing a rate increase.

The second accident happened on November 21st, when we were T-boned by an elderly driver. Their insurance has already accepted liability, so we would file all claims related to that accident under their coverage.

Currently, the car is at the body shop, where it has been since last Tuesday. Based on their estimates, the damage will likely deem the car a total loss, with repair costs around $27,000. Even separately, the damage from each individual accident would also be enough to consider the car a total loss.

My question is: To avoid paying the deductible and having her insurance rates increase, can we make just one claim against the at-fault driver's insurance from the second accident, or are we required to file two separate claims?