My car was totaled by a drunk driver, should I ask for a rental car?

Not sure I understand.  Another driver totalled your car by driving it or running into it? If the former and you knew this person was drunk, you may not be able to collect anything from your insurance company since I believe there may be some limiting provisions within your agreement.  However, if a drunk driver hit your car, you are not at fault and you need to file a claim through your insurance company and his.  Further, you may wish to review the damages because if indeed your car was totaled, you are really only entitled to what the car was worth when totaled.  I don't think it would be unreasonable to ask both his and your insurance company for reasonable car rental fees.

Whether you get a rental car depends on whether you (or your parents, if under their insurance) had insurance that included rental coverage. There is nothing in the law that provides a rental or replacement vehicle to drivers, regardless of age. If you feel the other driver was at faul (a DUI probably is), if you sue them, you can sue them for costs the cost to rent a car while between vehicles, as well as for the replacement value of your car; however, you only get the money when/if you win, not upfront, so it may be quite some time before you see this money, no matter how good your case. (If you are going to sue, therefore, it's better to do it right away.)

Note that if the drunk had property damage liability coverage, you're in an excellent position to recover the lower of (1) the value of your car and other costs; or (2) the limits of their insurance. (i.e. you can recover damages up to the insurance limits. But you still need to sue, or least let them know that you're going to sue, to get the money; the insurer will not come forward to volunteer the money to you. An attorney would be very helpful.