Your rates will not go up when you file a claim. People mistake the car side of insurance and home sometimes. What happens is if you have a claim, and you go to a new company, then you will start to pay more.
As for the claim, you might be better off to. If there is some dmg. you can not see, and that dmg does more dmg, you could get in trouble there.
Say there is a hole and water gets in somewhere. 6 months from now you find this out. You as the home owner did not mitigate your dmgs and now because of that, the org dmg caused more dmg. Could deny the claim.
I handle claim all day long and I am glad you do not have much dmg or anyone was hurt. I have seen some crazy stuff so far today!
Good luck, sure you will get lots of responses