Traumatophobia is the most commonly used term to describe a fear of injury, but there are different phobia names for different types of injury.
Myxophobia
Petsetaphobia - Fear of a towel or of being hit by a towel
Isolophobia.
Social Anxiety?
social phobia
There is no scientific name for being scared of carrots.
Because they were hurt or injured in someway in the past or they fear being hurt or taking advantage of by others.
I would call it isolosomniphobia- isolophobia is fear of being alone, and somniphobia is fear of sleeping. You seem to have a mixture.
There is no official term for that specific condition.But since the fear of pain is agliophobia, and the fear of heat is thermophobia, one could probably combine those to form the word thermagliophobia, which would roughly indicate the fear of pain from heat.
You call your insurance company
How we can stop a person being injured
No such phobia exists however, a fear of "everything" does and is called Pantophobia, Panphobia, Panophobia or Omniphobia. Also considered a medical condition and here's a tidbit; it's Greek from 'pan' and 'phobos'.