It is good to hear that you were not harmed in your single car accident with the tree. You would need to have collision coverage on your vehicle in order to have the damages to your car repaired by your insurance company. Collision has a deductible which you would have chosen at the inception of your policy.
You would need to have purchased rental vehicle coverage in order for your insurance company to provide you with a rental car allowance or reimbursement.
Review your policy before you rent a vehicle. Although policy limits vary, normally the company pays up to a specified amount per day for a specified number of days. The coverage usually ends when your vehicle is repaired, the loss is paid, or after the specified period, whichever comes first.
To find out if your policy coverages will over your car's repairs and a rental car read through your policy and talk to your agent. If you have the right coverages in place then you should be able to place a claim with your insurance carrier.