Can I sue for personal damages, medical expenses and loss wages after I was rear ended?

I was rear ended by a commercial truck driver. I have $4000 worth of damage to my vehicle. My insurance picked up the bill due to his company denying fault. He was cited and he was held 75% liable and me 25%. I have injuries. I had severe whiplash and cervical disc herniation. I have medical bills polling up and my car insurance is going to take care of it. My adjuster said I was liable even though the police report does not put me at fault. The driver who hit me was charged with failure to reduce speed. I have been out of work for 3 weeks. I am still in pain and still going to a chiropractor 3 times a week. Can I sue the other driver who was driving and was labeled at fault based off of the police report? I am not fighting my insurance company because they said I was negligent in the accident as well but majority the other driver’s fault no matter what the police report says. The driver even admitted fault and said he was not paying attention but lied to his insurance company. What can I do about my bills and all the money lost?