I did wudu for prayer, and during the prayer I remembered that I had not rinsed my nose. What is the ruling concerning my wudu and my prayer in this case?

Rinsing the nose in wudu is obligatory, because it is proven that the Prophet (peace and blessings of Allah be upon him) did this and said: “Whoever does wudu, let him rinse his nose.” Whoever does not rinse his nose, his wudu is not valid. So you must repeat both your wudu and your prayer.