Would the insurance company pay for the damage on my car?

My husband and I own a 2007 Jeep Grand Cherokee .It is in both our names and we are both insured under our insurance company.My husband is the primary holder. As I was getting out of the garage in our building (the ones that you turn in circles from one floor to another), I was making a turn and hit into the wall on my right.Both right doors are badly damaged. Would my insurance company pay for the damage?Even if it was in the garage? I know most likely I would have to pay the deductible and my insurance rate will go up ,but will the insurance pick up what I have to pay to fix it?It will cost at least 2000$.
The issue is that my drivers license is only 4 years old so I am concerned that if I am considered an inexperienced operator, will they still pay?Our insurance is already high to begin with and am very concerned since i cannot afford to pay over 2000$ right now.

Any advice will be appreciated.
Thank you