How exactly to track my life and not die

It's easy to miss if you're not aware, but every hero has an audio indicator when they drop to low health (typically a gasping intake of breath and a heartbeat, but it can vary). The audio is different for each hero so you'll need to train yourself to listen out for different things while playing different characters.

If you plug "overwatch critical health sounds" into your favourite search engine, you should get a good bit more information on them.

Instead of focusing so much on the crosshair, your eyes should be wondering around, checking skill cooldowns, your team's ult status(by pressing tab), and of course checking HP.

When a pro Winston like Miro leaves with just 50 HP, he isn't just guessing that he has low HP. He is looking at his health bar constantly and checking them. It helps that Winston doesn't require precise aiming, so your eyes can wonder around a bit.