If you have collision coverage,
you will be able to file a claim and get your damage repaired. But you are right - you won't be able to file these on one single claim. Meaning, you will have 2 at-fault accidents on your insurance record. Now, most insurance companies will continue to charge you for 3 years. In Florida,
an at-fault accident raised premiums an average of 37%.
So, when thinking if you should file a claim, you should consider if that 37% over 3 years is greater than your deductibles (you would be paying 2 in this example). Best of luck.