There is nothing wrong with praying for relief from harm and there is no contradiction between offering du’a for healing and being patient.

The Du`a of the fasting person that is answered is that which he offers whilst he is fasting, until he starts to break his fast, and not after that. As for the Dhikr, ‘Dhahaba Al-Dhama’u wabb talat Al-`uruq wa thabata Al-ajr in sha Allah’, it can only be said after breaking the fast.