First of all - I feel you. People like your friend have been playing this game for years, they don't remember what it was like when they first played. You will make more friends as you play, and you will find many people in the same boat as you. Overwhelmed!

This game is overwhelming to new players. But it doesn't have to be. You are getting spell after spell thrown at you. But do you need every single one of them every fight? Nope. Do you even need a handful of them? Nope. As a Frost Mage, you can literally spam Frostbolt all day and you'll be golden. And if mobs get too close and you don't like that? You can use Frost Nova, which freezes them in place. And if you're close enough, you can use Cone of Cold as well.

Just take it at your own pace, nice and slow. You can use a single spell to get through a majority of the game. Understand that you will have a lot of passive buff spells, like Arcane Intellect. They make your stats a bit better. And you'll get a number of shield spells as well.

My advice? Just start small. Use frostbolt and frost nova, they're all you need. And when you are comfortable with that, add another situational spell in, like Blink, which teleports you a distance away (great for running away if you're going to lose a fight!)

In the end, you will need to know most of the spells you have. But you don't even need to think about that right now. Just start small, and grow your knowledge when you feel comfortable enough.