Is it normal i'm constantly worried about my loved ones' deaths?

I was like this ever since I knew what death was. I remember, when I was younger, I hated waking up early in the holidays because I'd spend the whole morning worrying about my dad and why he wasn't awake yet. (It also didn't help that he usually slept in until 3pm or later, too.)

This continued, even as I got older. I recently moved into an apartment a few months ago, decent place, but lately those fears have been coming back. It's probably because I've been stressed out by a ton of little things but it's got so bad that I've had to make frantic, tearful calls in the middle of the fucking night to make sure he's okay. Sometimes he's (very understandably) annoyed about it but mostly he just tries to calm me down and says I can visit whenever.

I'm thinking of doing that, actually, although it'll be a bit of a pain to get the train and I'm sort of short on cash as it is. Should I do it anyway? Any advice about this is welcome.

So, IIN?

Side note: it might also be because my dad's a bit, well, older than most dads. He was 51 years old when I was born. Also, it's not just him, I'm worried a lot about my cat too. That's even more silly since he's only 3 years old and very healthy - never had an illness in his life.