

I would say it means strong but with an implied sadness, but you can have positive poignant memories too - you’d just have to state they were positive. The day I graduated from University was poignant because it was the end of an era and the start of another, but it doesn’t mean it is a sad memory.
That would depend whether you took a day off sick or just… a day off. If it’s a day off then you can spend it however you like, but I agree it can cause awkward questions if you are off sick but are seen.