Was the small stick attached to your hand?
If not then let her TRY to win in a court room! LOL! It's not gonna happen in my opinion.
My neighbour was hit by a small stick from my tree. I am worried she will take legal action?
Check on her, be friendly and if necessary offer to pay reasonable medical cost.
I would check on her and see what you can do. Id say not to worry about it but there are some scummy lawyers.
These are all suggestions. Look over your homeowners insurance and see if they pay for mishaps on your property. If it happened on hers but your tree is overhanging than take a picture of it as it stands and have someone cut it back.
Some people are sue happy, some people want someone to actively take responsibility of anything caused by something or someone who is the cause of discomfort or distress.
If you had a tree that was overgrown and a branch broke and caused me to go to the hospital. I would expect you to check on me, offer to pay and actually pay for my medical bills, and get your tree off my property. I personally wouldn't sue. If however my medical bills were high, and you ignore me or the tree, I'd look into suing. Not for pain and suffering, but payed medical bills and the removal of the tree. I would expect you to make me "whole" again, nothing less, nothing more. I wouldn't expect a payday. A lot of times people who go through the headache of suing do so because they are either looking for a payday, or were completely ignored by the offender.
Unless you knew that the "stick" was a potential hazard and did nothing about it ... Your neighbor would have no grounds to sue you.
Maybe, maybe not.
Years ago our youngest had a friend over to play (both about 11 years old).
Our son came flying in the back door. His friend was drinking a soda. The can hit his tooth and chipped it.
I immediately told his mother I would call my insurance company and they would pay to have the tooth fixed.
I did, they did, and she took him to the dentist.
S**T happens---that's why you have homeowners insurance.