How do I build a good defense for character in Skyrim?
I've found that the easiest way to stop your character getting dominated in big fights is to pump up your health each level increase.
On my last character, I was playing an archer whom I assumed would rarely get into a close-combat situation that I couldn't just kite out of. I spent each level increase on stamina so I could run further (as part of the hit-and-run tactic I was trying). It was great, except for every so often when I'd come up against something that pinned me down or shot at me from a distance. I was about to restart, but instead started investing in more health. All of a sudden, the game started to get easier. That character got to level 51 with over 300 health.
Other tips would be:
Invest in skills that increase your base damage for your weapon type. For example, maxing out the base skill for one-handed doubles your damage every single hit.
If you're looking for superior equipment, invest some skills in Smithing. If you go along the RIGHT hand side of the skill tree, you can craft the strongest weapons/armour for a light or heavy fighter or archer and improve them to legendary quality.
For fights against dragons and powerful enemies, keep some potions of fortify archery/one-handed/two-handed/destruction or whatever you're using to increase your damage. The sooner they die, the less damage they can do.
Carry potions of restore health attached to a hotkey so you can quickly restore health if you need to (if on the PC version, "favourite" them in the items menu, then press Q when out of the menu to open your favourites list. Move the selection over the item and press 1-8 to attach it to that hotkey).
Carry potions of resist frost/fire/shock/magic. A resistance of 40% almost halves the damage an enemy relying on that type of damage can do.
You can save money if you make these potions yourself. Consider investing some points in Alchemy (just the base skill, physician and benefactor is enough. Print an alchemy effects guide to find out what ingredients do, or just eat one of each ingredient to find an effect, then discover the rest through trial and error). Restore health, for instance, can be made quite simply with Blisterwort or Blue Mountain Flowers and Wheat.
If you rely on melee weapons, consider carrying a reasonable bow and some arrows (the arrows are weightless, the bow is fairly light too). In some situations, jumping on top of some rubble and shooting that warhammer-wielding master vampire is the smartest choice.
Let your companion attract the attention of nearby enemies and take the hits. They sound like a jerk for letting you die so often anyway. Target an enemy that is attacking your companion, so that you get a few hits in before they even realise they're being attacked by someone else.
If you let us know what character type you're playing, we can give more specific advice. Hope this helps for now.