..and when I fall ill, He is the One who restores me to health.
I fall ill, There is a very delicate point here; the respect and care that the Prophets'/Messengers' of Allah pay towards Allah (swt.)
Abraham/Ibraheem (peace be upon him) does not say "when Allah makes me ill" rather he says "when I fall ill", therefore not directly attributing his illness to Allah swt. Though he knows well that both health and illness is from Allah (swt). However because we all look at illness as a test, a trial, something difficult, so from the amount of respect he has for Allah (swt), he does not say when Allah makes me sick, but rather he acknowledges his illness as his fault.
Then he continues, to say that Allah (swt) is the one who restores his health (i.e. attributing the good to Allah). Giving Allah (swt) the prestige, and position of goodness. يَشْفِينِ this is in a tense that demonstrate that it will happen more than once. So on the one hand Abraham/Ibraheem says when I fall ill, meaning he knows he will, then he acknowledges that Allah (swt) will give him shifa [cure] more than once.
It is due to the goodness of his heart and the goodness that he exhibited in his character, that Allah (swt) chose him - Abraham/Ibrahim - as His khaleel [close friend].
All these mannerisms of Prophet Ibrahim/Abraham towards Allah are described in just 5 words!