Like an idiot, I chose this path to gain entrance into the College of Winterhold. The elf at the gate of the college wants me to cast a healing hands spell on her. Needless to say I can't find this spell anywhere. Can anyone point me in the right direction?

I think I bought mine from the mage in Dragonreach. But try the mage in the winterhold inn at the edge of town. bet he sells it.

If you tell her you don't have the spell she should offer to sell it to you for 30 gold.

This, or if you feel like paying extra money for no reason, go to dragonsreach, you can buy it from the Court wizard there.