Ok so I built a Dunmer warrior mage - skill focus on conjuration (conjured help and bound weapons), destruction, enchantment, one handed and light armor.

I am now around level 14, playing on master difficulty I think. I have pretty much alternated leveling magicka and health 60/40 or so. The way I intended to play this guy is to either raise an undead or summon an atronach to help me defeat an enemy and then lay into it with destruction magic, then once I am spent, go into melee. Well everything works fine until I get into the melee. Most times I am ok, but there are certain creatures I encounter now and then (falmer, sabretooth cats, etc.) that can lay me out in 2 hits. If they choose to ignore my summon and come straight for me, going into melee is not a viable option. Besides that my weapons don't seem to be affecting them that well either.

I am wondering if my equipment is the problem - for the most part I still am wearing the light imperial armor I found at the start of the game. I was using a bound sword until it started to become too magicka intensive and my conjuration was shooting way past my other skills. Right now I am like 44 conjuration, 35 destruction, 33 enchant, 39 one handed, and 34 light armor.

Am I just playing this type wrong? As an example - I was in Glimmerdust Cave (I think) the one with lots of falmer in it near Whiterun and at the end I encountered a Falmer Gloomlurker who can kill me easily with either its ice magic or its small dagger. The undead falmer I raised (that gave me a great deal of trouble) doesn't help much against it.

What am I doing wrong?

You're not doing anything wrong, Falmer are just strong. So are Sabre Tooth Cats.

Most people believe that everything in Skyrim scales with you, but that's not really the case. The game just "picks" enemies closest to your current level from a given type. If generic Falmer are all, say, level 14, then you will still get the same Level 14 Falmer whether you're level 1 or 14.

If you went straight to master and didn't try at least adept first there is one problem. Master level is really hard unless you really focus on one type of attacking, i.e destruction or melee e.t.c. To be an all-rounder at master you really need to know what you are doing. As for light armour, you could go naked and still survive easy enough, but if you are at levle 14 and haven't found better armour you could just try shopping for it. Make sure to put the Dunmer's Ancestor Wrath to good use too. I'm no expert on melee but i'm able to survive on master as a melee. Would be good to know if your one-handed, two-handed or dual-wielding as tactics can be different.

Try using Become Ethereal, that gives you time to use the environment to your advantage in an emergency. You might want to start using a shield. Makes melee easier and more fun.