Car was backed into and now the other driver won’t respond ?

Your insurance has an adjuster. Didn't they look at your car? It can take a month. or more. Just keep calling your insurance & ask to speak to someone in claims.

Okay....Use your own collision insurance.  Okay Your deductible will be returned to you when your own insurance company settles this. Okay

 Writing something "very fast" does not excuse poor grammar.

"I were at work" ?

Okay

If you have collision insurance, use it.  If you identify the liability carrier your insurance company can compel the other company to participate in compulsory arbitration.  When you win, you get your deductible back.

This is how "it" works.  Your company pays you minus the deductible.  You can then either sue the other driver (in Small Claims Court) for your deductible, OR you can authorize your insurance company to collect the full amount (including the deductible) from the other insurance company and refund your deductible to you.

This is very common.

The Police Report has nothing to do with insurance.  Police are after the fact witnesses, and the Report has little to do with any insurance company's determination of fault.

I’m assuming they were female

a) It's "I WAS backed into...", not "I were backed into...". Fail. 

.

b) It's up to your insurance company to follow up on this. That's partly what you're paying for when you have full coverage. BUT, you misunderstood something important. No matter who is at fault YOU have to pay the deductible. The only way to get reimbursed for that is to "subrogate" the claim. That is something you must ask your insurance company to do on your behalf if you don't want to retain a lawyer.  

"I were"? No, it's "I was". You can't control what the other driver or his insurance company does. Pay your deductible, get you car fixed, then your insurance company will go after the other insurance company and you should end up getting your deductible back. 

Give the Police report to your insurance company or gent and they will go after the other person's insurance company.

IF you made no police report at the time, you  are left with no option but to file with your insurance and then sue the other  party if he wont contact his insurance.  You can sue him in small claims court if you know their identity.