You can run smartctl (install smartmontools if you dont have it) or possibly udisks to find out what shape the drive is in.
Both rely on s.m.a.r.t. technology which is built into the drive-- it can help, though it doesn't always tell you what you need to know. (It's not perfect all of the time.)
Dropping to the (initramfs) prompt doesn't necessarily mean the drive is failing (it could mean that, if it is happening more and more often.) It could also mean that the system wasn't shut down properly-- for example if you were running on battery and it just shut off. The system will normally recover from that automatically, but sometimes it doesn't.
initramfs is one of the early stages of booting, it's the smaller system that is used to load the larger system:
stage 1: bios/uefi -> bootloader
stage 2: kernel, initramfs, init system
stage 3: the rest of the system
You could have a system that's very modest, fit entirely into the initramfs. However, that's not conventional or practical for most operating system setups.