Uninsured Motorist - How should I proceed?

State of Texas.

I was rear-ended (other driver at fault.) At time of accident, took driver's license information, insurance information, and license plate number. The other driver said he wanted to pay out of pocket, so I got estimates and called him. He started avoiding me so I called to make a claim on his insurance.

Come to find out, he had only paid for one month and then let his policy cancel, so the card was not valid. He is uninsured.

I DO have uninsured motorist on my insurance, but I am hesitant to file because I don't want my rates to go up for an accident that wasn't my fault.

Questions:

1. Can I sue based on estimates, or do I have to pay out of my pocket first before I can get an award in court?

2. Do insurance companies raise rates based upon uninsured motorist claims?

3. Is there a way to find out if this guy has insurance through another company?

Any advice on how to proceed will be greatly appreciated.