I'm in the same boat as you (freaked out by spiders, and unfortunately playing on xbox) - so far I've only done one quest in the game, and it involved a dungeon with some large spiders. The worst moment for me was a room that contained one very large spider...
I am playing a Breton mage, which gave me an advantage in this fight. First I cast "Summon Familiar" - my wolf ran toward the spider and engaged it in battle. While the spider was distracted, I ran around behind it and blasted it with fire. By the time it had killed my wolf and was just starting to turn around to face me, it was dead from my fire spell.
This strategy isn't helpful for dealing with spiders if you're not also playing a mage, but maybe you could get a follower and just let
them deal with the spiders you encounter.
I also freaked myself out by testing a "raise dead" spell on it - I actually didn't think it would work on that spider because it was like a boss...and the spell said it would work only on very weak dead monsters. But suddenly the spider rose up. I ran frantically into a small hallway and the spider couldn't follow, so I got brave and started whacking its legs with an iron sword. It started shooting some kind of spell (or webs?) at me so I ran all the way through the passageway to get away from it LOL.
