I suspect you probably lost some plywood, felt, gutter, and shingles as well.
Here is how I believe the insurance would work. Since it is your property, you file a claim with your insurance company. They will send an adjuster who will note the cause as neighbor at fault. Same is true if the wind blew a DEAD tree into your house (neighbor at fault hint hint all you neighbors with nuisance dead trees!) Live wind blown trees are a different story. Anyway back to your problem. Your insurance will then go after your neighbor. Unless you can talk your neighbor into paying your deductible, your on the hook for that. The insurance company and in turn the mortgage company will frown on a DIY repair job unless you can prove it was done properly as Glenn describes above. They will likely want the work done by a pro. If the claim is above about $2000 there will be a industry wide insurance record of claim on your property that lasts I believe indefinetly and transfers with ownership and from insurance company to insurance company. Its a nationwide database that ins. companies participate in. Kind of like a carfax report for your home.
What I am saying is do it right because if insurance is involved a prospective home owner who wants to buy your home will find out when he goes through the process and will want his home inspector to concentrate on that area or give up on your home entirely.
Can you attach a picture? There are a couple of home inspectors and other pros on this site who probably tell at a glance if it can be pulled off as a DIY or if you should get a pro.