If you are able to just keep your head down and get your work done and seem competent enough, I would probably lean that way. But it seems like this is really having an impact on your work in a new job, so it may be worth it to speak to your boss about this. However, it would be a lot more preferable if this were a boss you knew well in a job you had been at longer.

I would consider saying something like, "I had kind of a tough training day the other day, and I wanted to let you know that I realized that, and I'm trying to be more focused. My parents are going through kind of a rough period with a health issue, and it's been taking some of my attention and focus, and it's been on my mind a lot. I wanted to share that because I didn't want you to think that you made a bad hire or I can't keep up with the training or anything, I'm just going through kind of a temporary rough patch, but I'll work through it."

Im would keep it vague as "heath issue," and if your boss asks for details or asks if it's cancer or something, you can just say you'd prefer not to say because it's their health and their privacy.