I'm level 16, and I prefer swords over maces / war axes but I haven't found a single sword in game that has better damage rating than the maces / axes I have. Is it something about where the game takes place, like in Skyrim axes are more favored than swords?

You won't find a higher damaging sword than mace or axe, in the sense that an Iron mace has more base damage than an Iron Sword, Steel Mace more than Steel Sword, Dwarven Mace more than Dwarven Sword, etc. But swords swing faster than maces and axes, so their DPS (damage per second) ends up being about the same. This is just an example, but say a sword swings twice as fast as a mace but only does 1/2 the damage per hit, you still end up doing the same damage over all. That's what's going on here: it's not 1/2, it's more like 83%, but the point is the same. Axes do more damage per hit than swords, but swords swing and hit more often. Maces are the slowest, but hit for the most damage. But again, in the end it all pretty much balances out. It up to your play style. If you like swords more than maxes or axes, stick to them. You aren't using an inferior weapon if you use swords. I only use swords, if that makes you feel a little better.

Edit: Clarification and Spelling

Swords are the fastest; they will NEVER have a higher base damage than an axe or mace.

It depends what you spec-ed into. If you put your perks into sword skills, use swords. If you put them into axes or maces, use those.

Simple! Craft your own sword and upgrade it at a grindston, if you put some effort into your weapons you can defeat anything!

You will eventually find a Daedra shrine, that gives you a pretty damn epic sword.

Or do the thieves guild, you get a good sword along the way, I won't mention names or which Daedra shrine otherwise it'll be a dirty spoiler.

P.S If you wanted to switch to two-handed at any point do the Companions, you get a really good two-hander early on. I am still using it now over my Daedra weapons, ebony and Daedric at level 41, WUUTHRAD!

swords are fast-and-weak. axes are middleground. maces are slow-and-strong.

Swords will always be weakest. I prefer them for their extra speed.

I thought it odd that the artifact sword I found had less damage than my crafted orcish mace.