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Thank you for your question.
First of all, it does not matter that your tires were in a no parking zone. Your neighbor is responsible because she is the one who caused the damage.
Your insurance policy has a $1,000 deductible, which means that you pay for the repairs yourself if it is under $1,000.00 and then your insurance company will pay for any claims after that during the same year.
The best thing to do would be to (1) go get the car repaired and then (2) sue for the cost in small claims court.
If you cannot afford to repair the car, then you need to go ahead and sue in small claims and take a few estimates with you as proof of how much it will cost to have the car repaired.
Please let me know if you have further questions regarding this matter.