What is the ruling on a nurse drawing blood from a man while wearing gloves, and is that permissible?

The general rule is that men should treat men and women should treat women, except when there is a need. There is no blame upon you for what you did, as long as you inquired about the availability of a male nurse and found none, and no private seclusion occurred, especially if the female nurse wore gloves. Your rejection of such matters is commendable. However, the hatred you feel towards the calls of the people of falsehood should not lead you to exaggerate in matters concerning women. What is obligatory is to adhere to the limits and etiquettes of Islamic law and to seek Allah's pleasure.