Explaining a gap after caregiving or layoff - 3 months and counting

My résumé shows a gap from a layoff and some health issues. It has been weighing on me all week. I am nervous about being filtered out. What do you say in interviews?

Thanks for writing this out. I went through something close to it 3 months ago, and it settled down once I kept a simple log of every call and form.

I was hired after a 3-month gap. The manager said the skills test mattered more than the dates.