I just spent an hour training and improving a bunch of my skills, and got my butt handed to me when I fought someone from an area I had been to before. They both were girls, but the first had rags, and now she had a shield and mace.

Some of the content scales with you and some of it doesn't.

Its a good move to increase combat perks in between non combat perks to keep it balanced, if you improve too many non combat perks in a row you may find things harder.

Thats the thing, I only improved my shielding and heavy armor, and now things are way too freaking hard. Should i be improving my one-hander?

It does scale with you yes. For example, in the Todd Howard Demo, while in Bleakfall barrows he fights a troll on an ice bridge. Many people complained or were just upset when they arrived around level 5 or 6 to find a simple skeleton/draughr (cant remember which) on that bridge. I entered bleakfall barrows on my current character at level 30. There was indeed a troll on the bridge instead. I've noticed many things like this.

So to answer your question, yes.