How do I heal myself?

Recoveries are less like healing and a bit more like "extra lives". From Wikipedia:

If the player's health is reduced to 0, they can use a Recovery that instantly recovers to full health. Recoveries can be acquired by gathering cell samples left behind by killed creatures (including Humans or Na'vi) or plants, but only 5 Recoveries can be carried at any one time.

So if you keep dying, it's because you haven't acquired any Recoveries from cell samples yet (or you've fallen to an unavoidable death). There isn't another way to heal. Start sciencing those alien flora and fauna!