This is very common. If it's a CHP report, the report is often ready within 7 – 10 days. If the report is from the Los Angeles Police Department, it will take on average three months. Yes, three months. The police department, sheriff's department, or CHP office can tell you approximately how long until the report is ready. What do you do in the meantime?
As to your property damage: I suggest you go through your auto insurance, if you have collision coverage under your policy. You will have to pay the deductible, but you will get that reimbursed assuming that the other driver has auto insurance and his insurance company accepts fault for the accident. If you don't have collision coverage under your policy, then you will have to wait until the police report is ready to see if the other driver has insurance. If your vehicle is at an impound yard incurring daily impound fees, you can either pay the impound bill and remove the vehicle from the impound yard and have it towed to your residence, or you can leave the vehicle at the impound yard. Eventually, if the vehicle is not removed, the impound yard will lien sale the vehicle to pay off the impound fees. Once you find out who the other driver's insurance carrier is, you can open a property damage claim with them.
As to your injury claim: If you were injured, I suggest you go through your health insurance to get medical treatment, assuming you have health insurance. You don't want to delay treating while you wait for the police report. Any delay in getting treatment will be used against you by the other driver's insurance company, who will argue that if you were really hurt, you would have treated right away.
If it turns out that the other driver was uninsured, you can make an injury claim under your own uninsured motorist coverage, assuming you have it. You need not worry that making such a claim will cause your premiums to go up or cause your policy to be cancelled. As long as you were not at fault for the accident, making an uninsured motorist claim will have zero effect on your premiums or renewability.
If you don't have uninsured motorist coverage, and it turns out that the other driver was uninsured, then you will likely be unable to pursue an injury claim against the other driver. The other driver is legally on the hook for your injuries and bills (medical bills, lost wages, property damage, etc.), but the reality is, if the other driver has no auto insurance, he probably has no assets to go after, or he would have purchased auto insurance.
I recommend that you consult with a car accident lawyer, sooner rather than later, to get advice. You don't want to do anything that will negatively impact the value of your claim. You are welcome to call our firm for a free consultation. Even if you do not hire our firm, we are happy to give you advice on what to do. If you do hire us, and it turns out that the other driver was uninsured and you have no uninsured motorist coverage, you pay us nothing if we end up collecting no money for you. This is our "No Fee Promise."