Just a little update. I called my insurance and they in fact do not waive the deductible, even if the other party is at fault. And I don't have uninsured motorists because my insurance is already $300 a month. My deductible is so high because I had no idea I'd ever get into a wreck because I'm a safe driver. Little did I know you can get into an accident even so due to the carelessness of other drivers.
I called their insurance and was told they could not find the driver under a policy.
(That would explain the wait but why wasn't I made aware until I called) I then was able to get a hold of the police officer who came to the scene and he kindly emailed me the police report with all the information including their insurance. I emailed it to claims just now.